or columns of the image. The image is filtered by inverse filters derived from the models, generating as many channels (residuals) as the number of textures classes. The joint distribution of the filters outputs is considered for each class. The image is classified on a pixel by pixel basis using a maximum likelihood classifier or on a sample basis (set of connected pixels) using the JM-distance, sample maximum likelihood or majority criteria. A new sample classifier, based on distances defined over two-dimensional autocorrelation functions, is also proposed. The methods were tested using synthetic aperture radar (SAR), Brodatz' book and SPOT panchromatic images. The obtained models for the defined classes were presented and discussed, relating them to the characteristics of the textures and the formation process of the image. The classification results showed substantial improvement of the average performance (an estimation of the correct classification probability) mainly for the cases in which the differences of classes means were negligible. Good performance was also verified using the sample classifier based on distances between two-dimensional autocorrelation functions. Author N91-11422# Instituto de Pesquisas Espaciais, Sao Jose dos PERFORMANCE COMPARISON OF EDGE DEFECTION DESEMPENHO DE DETETORES DE BORDA MORFOLOGICOS] (INPE-5012-TDL/400) Avail: NTIS HC/MF A05 The problem of edge detections is of fundamental importance in digital image processing. The performance of edge detectors derived from mathematical morphology is studied. In particular, the performance of six different types of morphological detectors is evaluated. The detectors are known as erosion residue (Ge), dilation residue (Gd), maximum combined (Gmax), minimum combined (Gmin), sum combined (Gsum) and blue and minimum operator (Gblur). These detectors are visually evaluated through simulated image and real satellite images. Quantitative evaluation of these detectors, with respect to edge shift, both horizontal and diagonal, and edge orientation is also presented. Author N91-11423# Instituto de Pesquisas Espaciais, Sao Jose dos GEOMETRIC CORRECTION OF SPOT IMAGERY WITH THE (INPE-5014-TDL/401) Avail: NTIS HC/MF A06 A theoretical and practical methodology is described for geometric correction of satellite imagery including effects of relief. The methodology presented is applicable over the unfavorable situations, such as images obtained in lateral view with large inclination angle and pronounced height differences. The images already corrected must be superposed to a topographic map at the scale of 1:50,000 or smaller. The SPOT sensor was chosen in face of the possibility of lateral views, which emphasized the relief displacement. The correction process uses ephemeris and attitude data, ground control points, collinearity equations, and a digital elevation model. The implementation is done in a microcomputer environment and uses some functions of the Image Processing System (SITM) and the Geographic Information System (GIS) developed at the Brazilian Space Research Institute. THE APPLICATION OF TRAJECTORY PREDICTION J. N. P. Beers, T. B. Dalm, J. M. tenHave, and H. Visscher Copyright Avail: NTIS HC/MF A20; Non-NATO Nationals requests available only from AGARD/Scientific Publications Executive 62 COMPUTER SYSTEMS Includes computer networks and special application computer systems. N91-11425*# Sterling Federal Systems, Inc., Palo Alto, CA. (NASA-CR-177561; A-90240; NAS 1.26:177561) Avail: NTIS The Open Systems Interconnection (OSI) protocol suite is a result of a world-wide effort to develop international standards for networking. OSI is formalized through the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC). The goal of OSI is to provide interoperability between network products without relying on one particular vendor, and to do so on a multinational basis. The National Institute for Standards and Technology (NIST) has developed a Government OSI Profile (GOSIP) that specified a subset of the OSI protocols as a Federal Information Processing Standard (FIPS 146). GOSIP compatibility has been adopted as the direction for all U.S. government networks. OSI is extremely diverse, and therefore adherence to a profile will facilitate interoperability within OSI networks. All major computer vendors have indicated current or future support of GOSIP-compliant OSI protocols in their products. The NASA Science Internet (NSI) is an operational network, serving user requirements under NASA's Office of Space Science and Applications. NSI consists of the Space Physics Analysis Network (SPAN) that uses the DECnet protocols and the NASA Science Network (NSN) that uses TCP/IP protocols. The NSI Project Office is currently working on an OSI integration analysis and strategy. A long-term goal is to integrate SPAN and NSN into one unified network service, using a full OSI protocol suite, which will support the OSSA user community. Author (CWI-BS-R8931; ETN-90-97664) Copyright Avail: NTIS HC/MF A03 The modeling and analysis of a class of computer systems whose primary task is the massive processing of batch transactions and are called Transaction Driven Computer Systems (TDCS's) are addressed. A generic queueing model for TDCS's is presented and the mean sojourn time experienced by the different transactions is calculated. The approach is to model a TDCS by a cyclic polling system with bulk arrivals, deterministic service times, limited-1 service and zero switch-over periods. Since the performance analysis of this polling model has not been provided before, the study concentrates on deriving mean delay approximations for it. The analysis is carried out for models with general switch-over periods, and a special case of it (zero switch-over periods) is suitable for analyzing a TDCS. ESA N91-11427# Center for Mathematics and Computer Science, B. P. Sommeijer, W. Couzy, and P. J. vanderHouwen Aug. 1989 12 P (CWI-NM-R8918; ETN-90-97673) Copyright Avail: NTIS HC/MF A03 The stability of a class of block methods which are suitable for use on parallel computers is studied. A-stable methods of orders 3 and 4 and A(alpha)-stable methods with alpha greater than 89.9 degrees of order 5 are constructed. On multiprocessor computers these methods are of the same computational complexity as implicit linear multistep methods on one-processor computers. ESA N91-11428# Center for Mathematics and Computer Science, P. J. vanderHouwen and B. P. Sommeijer Jan. 1990 29 p Diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers are studied. These iteration methods are such that after a finite number of m iterations, the iterated Runge-Kutta method belongs to the class of Diagonally Implicit Runge-Kutta methods (DIRK methods) using mk implicit stages where k is the number of stages of the generating implicit Runge-Kutta method (corrector method). However, a large number of the stages of this DIRK method can be computed in parallel, so that the number of stages that have to be computed sequentially is only m. The iteration parameters of the method are tuned in such a way as to get fast convergence to the stability characteristics of the corrector method. By means of numerical experiments it is shown that the solution produced by the resulting iteration method converges rapidly to the corrector solution so that both stability and accuracy characteristics are comparable with those of the corrector. This implies that the reduced accuracy often shown when integrating stiff problems by means of DIRK methods already available in the literature (which is caused by a low stage order), is not shown by the DIRK methods developed provided that the corrector method has a sufficiently high stage order. Moreover, by iterating e.g., Radau correctors, methods of any order can be constructed, whereas the order of accuracy of the conventionally constructed DIRK methods is limited to four. ESA N91-11429# Technische Univ., Delft (Netherlands). Faculty of A FAST PARALLEL RECOGNIZER Algorithms that can recognize a language described by a context free grammar are studied. The Gibbons and Rytter algorithm, which relies heavily on a pebble game theorem is given. A previous de Vreught and Honig time algorithm is recalled, and a fast parallel N91-11430*# Institute for Computer Applications in Science and Engineering, Hampton, VA. PARALLELIZED RELIABILITY ESTIMATION OF RECONFIGURABLE COMPUTER NETWORKS Final Report David M. Nicol, Subhendu Das (College of William and Mary, Williamsburg, VA.), and Dan Palumbo Sep. 1990 25 p Submitted for publication (Contract NAS1-18605; NAG1-787; NAG1-1132; NSF ASC-88-19373) (NASA-CR-182101; ICASE-90-60; NAS 1.26:182101) Avail: NTIS HC/MF A03 CSCL 09B A parallelized system, ASSURE, for computing the reliability of embedded avionics flight control systems which are able to reconfigure themselves in the event of failure is described. ASSURE accepts a grammar that describes a reliability semi-Markov state-space. From this it creates a parallel program that simultaneously generates and analyzes the state-space, placing upper and lower bounds on the probability of system failure. ASSURE is implemented on a 32-node Intel iPSC/860, and has achieved high processor efficiencies on real problems. Through a combination of improved algorithms, exploitation of parallelism, and use of an advanced microprocessor architecture, ASSURE has reduced the execution time on substantial problems by a factor of one thousand over previous workstation implementations. Furthermore, ASSURE's parallel execution rate on the iPSC/860 is an order of magnitude faster than its serial execution rate on a Cray-2 supercomputer. While dynamic load balancing is necessary for ASSURE's good performance, it is needed only infrequently; the particular method of load balancing used does not substantially affect performance. Author N91-11431# Oak Ridge National Lab., TN. Engineering Physics and Mathematics Div. ON THE ADEQUACY OF MESSAGE-PASSING PARALLEL Y. Y. Azmy 1990 8 p A coarse-grained, static-scheduling parallelization of the standard iterative scheme used for solving the discrete-ordinates approximation of the neutron transport equation is described. The parallel algorithm is based on a decomposition of the angular domain along the discrete ordinates, thus naturally producing a set of completely uncoupled systems of equations in each iteration. Implementation of the parallel code on Intcl's iPSC/2 hypercube, and solutions to test problems are presented as evidence of the high speedup and efficiency of the parallel code. The performance of the parallel code on the iPSC/2 is analyzed, and a model for the CPU time as a function of the problem size (order of angular quadrature) and the number of participating processors is developed and validated against measured CPU times. The performance model is used to speculate on the potential of massively parallel computers for significantly speeding up real-life transport calculations at acceptable efficiencies. We conclude that parallel computers with a few hundred processors are capable of producing large speedups at very high efficiencies in very large three-dimensional problems. DOE (NASA-CR-183963; NAS 1.26:183963; MCR-89-559) Avail: NTIS HC/MF A03 CSCL 09B Under the Intelligent Robotics System Study (IRSS) contract, a generalized robotic control architecture was developed for use with the ProtoFlight Manipulator Arm (PFMA). The controller built for the PFMA provides localized position based force control, teleoperation and advanced path recording and playback capabilities. Various hand controllers can be used with the system in conjunction with a synthetic time delay capability to provide a realistic test bed for typical satellite servicing tasks. The configuration of the IRSS system is illustrated and discussed. The PFMA has six computer controllable degrees of freedom (DOF) plus a seventh manually indexable DOF, making the manipulator a pseudo 7 DOF mechanism. Because the PFMA was not developed to operate in a gravity field, but rather in space, it is counter balanced at the shoulder, elbow and wrist and a spring counterbalance has been added near the wrist to provide additional support. Built with long slender intra-joint linkages, the PFMA has a workspace nearly 2 meters deep and possesses sufficient dexterity to perform numerous satellite servicing tasks. The manipulator is arranged in a shoulder-yaw, pitch, elbow-pitch, and wrist-pitch, yaw, roll configuration, with an indexable shoulder roll joint. Digital control of the PFMA is implemented using a variety of single board computers developed by Heurikon Corporation and other manufacturers. The IRSS controller is designed to be a multi-rate, multi-tasking system. Independent joint servos run at a 134 Hz rate and position based impedance control functions at 67 Hz. Autonomous path generation and hand controller inputs are processed at a 33 Hz. Author N91-11433 California Univ., Los Angeles. Avail: Univ. Microfilms Order No. DA9022003 The Linear/Quadratic (LQ) optimal control theory, introduced by Kalman, has attracted much attention due to the guaranteed control optimality with respect to a quadratic performance measure, and its inherent capability to handle Multiple-Input-Multiple Output (MIMO) systems. The LQ design process can be automated through an array of analytical procedures, greatly easing the design efforts. However, unsatisfactory performance and lack of robustness were experienced with the LQ design method. Numerous methods have been proposed in the past attempting to solve either the performance and/or the robustness problems of LQ optimal control theory. A method that combines the merits of time-domain and frequency-domain techniques for designing feedback control systems is studied. The approach involves the use of state augmentation to introduce dynamic compensators for performance enhancement first and, then, optimize a quadratic cost functional with the constraint of minimum multivariable stability margins. This robustness constrained optimization of quadratic performance measure approach is direct and matches well with the formulation and design objectives of real-life design problems. Multivariable examples of designing aircraft flight control laws with state feedback and output feedback are included to illustrate and demonstrate the effectiveness of the approach. The subject of how to augment the state of a dynamic system for performance enhancement is also examined from the standpoint of controllability, feedback equivalence, and minimum order. Dissert. Abstr. N91-11434# Oak Ridge National Lab., TN. Engineering Physics and Mathematics Div. A UNIFIED FRAMEWORK FOR CREDIT ASSIGNMENT Gunar E. Liepins and Richard S. Sutton (GTE Labs., Inc., Waltham, MA.) 1990 6 p Presented at the IEEE Conference on Neural Information Processing: Natural and Synthetic, Denver, CO, 26-29 Nov. 1990 (Contract DE-AC05-84OR-21400) (DE90-011636; CONF-901150-1) Avail: NTIS HC/MF A02 Credit assignment is a central issue in a variety of connectionist paradigms including artificial neural networks and genetic classifier systems. For neural networks, credit assignment is implicit in the training algorithms used to update connection weights. In classifier systems, it is used to estimate rule strengths. This paper introduces a unifying framework that covers and helps explain the differences and similarities between a large number of approaches to credit assignment, including Q-learning, policy iteration, bucket brigade and profit sharing. Each of these can be formulated as a version of the Adaptive Heuristic Critic (AHC). DOE N91-10929# Deutsche Forschungsanstalt fuer Luft- und Raumfahrt, Goettingen (Germany, F.R.). Inst. fuer Aeroelastik. ADAPTIVE DIGITAL REAL TIME FILTERING IN STRUCTURAL DYNAMICS: A CONTRIBUTION TO THE REALIZATION ON ACTIVELY REACTING ELASTIC STRUCTURES (ARES) [ADAPTIVE DIGITALE ECHTZEITFILTERUNG IN DER STRUKTURDYNAMIK: EIN BEITRAG ZUR REALISIERUNG AKTIV REAGIERENDER ELASTISCHER STRUKTUREN (ARES)] Roger Wimmel and Joerg Melcher In its Contributions in the Field of Aeroelastics on the Occasion of the 60th Anniversary of Professor Dr.-Ing. Habil. Hans Wilhelm Foersching Apr. 1990 p 187-202 In GERMAN; ENGLISH summary (For primary document see N91-10920 02-02) Avail: NTIS HC/MF A13 64 NUMERICAL ANALYSIS Includes iteration, difference equations, and numerical approximation. N91-11435# National Inst. of Standards and Technology, Gaithersburg, MD. Applied and Computational Mathematics Div. EXPECTED COMPLEXITY OF THE 3-DIMENSIONAL VORONOI DIAGRAM J. Bernal May 1990 21 p (PB90-221862; NISTIR-4321) Avail: NTIS HC/MF A03 CSCL 12A Let S be a set of n sites chosen independently from a uniform distribution in a cube in 3-D Euclidean space. Work by Bently, Weide, and Yao is extended to show that the Voronoi diagram for S has an expected O(n) number of faces. A consequence of the proof of this result is that the Voronoi diagram for S can be Author constructed in expected (9n) time. N91-11436# National Inst. of Standards and Technology, Gaithersburg, MD. Applied and Computational Mathematics Div. EXPECTED LINEAR 3-DIMENSIONAL VORONOI DIAGRAM ALGORITHM J. Bernal Jun. 1990 17 p (PB90-227984; NISTIR-4340) Avail: NTIS HC/MF A03 CSCL 12A Let S be a set of n sites chosen independently from a uniform distribution in a cube in 3-D Euclidean space. An expected O(n) algorithm for constructing the Voronoi diagram for S together with numerical results obtained from an implementation of the algorithm are presented. Author N91-11437# National Inst. of Standards and Technology, The integral I (sub 1,l')(k,K') = integral from 0 to infinity (j sub 1)(kr)(j sub l')(k'r) squared dr, in which the spherical Bessel functions (i sub l)(kr) are the radial eigenfunctions of the 3-D wave equation in spherical coordinates, is evaluated in terms of distribution, in particular step functions and delta functions. It is shown that the behavior of I (sub I,l') is very different in the cases I-l' even (0, + or -2,+ or -4,...) and l-l' odd (+ or -1, + or -3,...). For l-l' even, it is expressed in terms of the delta function, step function, and Legendre polynomials. For l-l' odd, it is expressed in terms of Legendre functions of the second kind and step functions; no delta functions appear. Author N91-11438# Center for Mathematics and Computer Science, APPROXIMATION OF THE SOLUTION TO THE MOMENT M. Zwaan Dec. 1989 13 p (CWI-AM-R8923; ETN-90-97653) Copyright Avail: NTIS HC/MF A03 A construction of the solution to a moment problem was obtained. The results are used to derive a truncation error for sinc-interpolation, which generalizes the error bounds in the literature to the case of nonuniform sampling. The space of bandlimited functions, those functions whose Fourier transforms have compact support, is introduced. ESA N91-11439# Center for Mathematics and Computer Science, MATHEMATICAL MORPHOLOGY ON HOMOGENEOUS J. B. T. M. Roerdink Dec. 1989 25 p A generalization of mathematical morphology by dropping the assumption that the invariance group is commutative is studied. To this end an arbitrary homogeneous space, a set on which a transitive but not necessarily commutative group of invertible transformations is defined, and considered. As the object space, the Boolean algebra of all subsets of this homogeneous space is taken. The case that the transformation group is simply transitive, or equivalently, that the basic set is itself a group, is considered. For clarity of exposition as well to emphasize the connection with classical Euclidean morphology, the study was restricted to the case of Boolean lattices, which is appropriate for binary image transformations. ESA N91-11440# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Analysis, Algebra, and Geometry. UNIFORM ASYMPTOTIC APPROXIMATION OF FERMI-DIRAC INTEGRALS N. M. Temme and A. B. Olde Daalhuis Jan. 1990 9 p (CWI-AM-R9001; ETN-90-97655) Copyright Avail: NTIS HC/MF A02 A given Fermi-Dirac integral is considered for large positive values of x and q. The results are obtained from a contour integral in the complex plane. The approximation contains a finite sum of simple terms, an incomplete gamma function, and an infinite asymptotic series. As follows from earlier results, the incomplete gamma function can be approximated in terms of an error function. ESA N91-11441# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Analysis, Algebra, and Geometry. DYNAMIC MRI RECONSTRUCTION AS A MOMENT PROBLEM. PART 3: AN ERROR ANALYSIS OF RECONSTRUCTION BY SINC AND SPLINE INTERPOLATION IN A HILBERT SPACE SETTING M. Zwaan Jan. 1990 22 p (CWI-AM-R9002-Pt-3; ETN-90-97656) Copyright Avail: NTIS HC/MF A03 A solution and an error analysis of a reconstruction problem that appears in Magnetic Resonance Imaging (MRI), which is a diagnostic technique to measure and display cross sections of human organs is given. The reconstruction problem is solved in the setting of L squared-spaces of vector valued functions. After obtaining the solution, error estimates are proved and the solution is shown to be stable for perturbation of the data and of the time markers. ESA N91-11442# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Analysis, Algebra, and Geometry. GREY-LEVEL MORPHOLOGY H. J. A. M. Heijmans Jan. 1990 31 p A detailed study of morphological operators on the space of grey-level functions is presented. It is shown how classical morphological operators for binary images can be extended to the space of grey-level images. Particular attention is given to the class of so-called flat operators, i.e., operators which commute with thresholding. It is also shown how to define dilations and erosions with non-flat structuring elements if the grey-level set is finite. ESA N91-11443# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Operations Research, Statistics, and System Theory. ON THE UNIQUENESS OF KERNELS A. Schrijver Oct. 1989 17 p (CWI-BS-R8924; ETN-90-97658) Copyright Avail: NTIS HC/MF A03 The case where S is a compact orientable surface is studied. For any graph G embedded on S and any closed curve D on S, (mu sub G)(D) is defined as the minimum number of intersections of G and D', where D' ranges over all closed curves freely homotopic to D. G is called a kernel if (mu sub G') does not equal (mu sub G) for each proper minor G' of G. It is proved that if G and G' are kernels with (mu sub G) equal to (mu sub G'), then G' can be obtained from G by a series of the following operations: homotopic shifts over S; taking the surface dual graph; replacing a vertex v of degree 3 by a triangle connecting the three vertices adjacent to v, or conversely. ESA N91-11444# Center for Mathematics and Computer Science, CONES OF MATRICES AND SETFUNCTIONS, AND 0-1 L. Lovasz (Eoetvoes Lorand Univ., Budapest, Hungary) and A. (CWI-BS-R8925; ETN-90-97659) Copyright Avail: NTIS HC/MF A03 It has been recognized that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. A general method to construct higher dimensional polyhedra (or, in some cases convex sets) whose the projection approximates the convex hull of 0-1 valued solutions of a system of linear inequalities is developed. An important feature of these approximations is that any linear objective function can be optimized over them in polynomial time. In the special case of the vertex packing polytope, a sequence of systems of inequalities, such that already the first system includes clique, odd hole, odd antihole, wheel, and orthogonality constraints is obtained. In particular, for perfect (and many other) graphs, this first system gives the vertex packing polytope. For various classes of graphs, including t-perfect graphs, it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets. An extension of the method, which establishes a connection with certain submodular functions and the Moebius function of a lattice, is discussed. N91-11445# Amsterdam ESA Center for Mathematics and Computer Science, (Netherlands). Dept. of Operations Research, Statistics, and System Theory. ON SLLN FOR MARTINGALES WITH DETERMINISTIC Kacha O. Dzhaparidze and Peter J. C. Spreij (Vrije Univ., (CWI-BS-R8933; ETN-90-97666) Copyright Avail: NTIS HC/MF A03 The Strong Law of Large Numbers (SLLN) is proved for multivariate martingales with deterministic quadratic variation, along the same lines as in Lai, Wei and Robbins (1979), though the setting here is more general. The problem still has a relatively simple solution under the restriction that the quadratic variation process of the multivariate martingale in question is deterministic. ESA N91-11446# Center for Mathematics and Computer Science, M. Kuijper and J. M. Schumacher (Tilburg Univ., Netherlands) (CWI-BS-R9002; ETN-90-97669) Copyright Avail: NTIS HC/MF A03 Necessary and sufficient conditions are derived for the minimality of descriptor representations under external equivalence. These conditions are stated completely in terms of the matrices E, A, B, C, and D. Use is made of the close connection between the descriptor representation and the so-called pencil representation. This connection is further exploited to derive the transformation group for minimal descriptor representations. The transformations are shown to coincide with the operations of strong equivalence as introduced by Verghese et al. ESA N91-11447# Center for Mathematics and Computer Science, A NEW LOWER BOUND FOR THE DE BRUIJN-NEWMAN H. J. J. teRiele Sep. 1989 11 p Submitted for publication A new lower bound, minus 5, is presented for the so-called de Bruijn-Newman constant. This constant is related to the Riemann hypothesis. The new bound is established by the high precision computation (with an accuracy of 250 decimal digits) of the coefficients of a so-called Jensen polynomial of degree 406, and the so-called Sturm sequence of this polynomial which shows that it has two complex zeros. These complex zeros are given explicitly. ESA N91-11448# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Numerical Analysis. IMPROVED TECHNIQUES FOR LOWER BOUNDS FOR ODD PERFECT NUMBERS R. P. Brent, G. Cohen (Sydney Univ., Australia ), and H. J. J. teRiele Oct. 1989 16 p Submitted for publication (CWI-NM-R8921; ETN-90-97675) Copyright Avail: NTIS HC/MF A03 If N is an odd perfect number and q to the power K parallel verticle lines N, q prime, k even, then it is almost immediate that N is greater than q to the power (2k). Subject to certain conditions verifiable in polynomial time, it is proved that in fact N is greater N91-11449# Center for Mathematics and Computer Science, Amsterdam (Netherlands). Dept. of Numerical Analysis. A STATIC-REGRIDDING METHOD FOR TWO-DIMENSIONAL PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS R. A. Trompert and J. G. Verwer Dec. 1989 30 p Submitted for publication (CWI-NM-R8923; ETN-90-97677) Copyright Avail: NTIS HC/MF A03 The field of numerical solution of time dependent partial differential equations is addressed. Attention is focussed on parabolic problems in two space dimensions the solutions of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and disappearing, layers. For such problems, a space grid held fixed throughout the entire calculation can be computationally inefficient, since, to afford an accurate approximation, such a grid would easily have to contain a very large number of nodes. A static-regridding method that adapts the space grid using nested, locally uniform grids, is considered. Several aspects occurring in such a static-regridding algorithm, such as the data structure, the regridding strategy and the determination of initial and boundary conditions at coarse-fine grid interfaces are discussed. Two numerical examples to demonstrate the performance of the method are presented: a hypothetical example to illustrate the convergence behavior of the method and an example originating from practice which describes a model combustion process. ESA N91-11450# Center for Mathematics and Computer Science, W. H. Hundsdorfer and B. I. Steininger (Gehrenbergstrasse, To prove convergence of numerical methods for stiff initial value problems, stability is needed but also estimates for the local errors which are not affected by stiffness. Global error bounds are derived for one-leg and linear multistep methods applied to classes of arbitrarily stiff, nonlinear initial value problems. It is shown that under suitable stability assumptions the multistep methods are convergent for stiff problems with the same order of convergence as for nonstiff problems, provided that the stepsize variation is sufficiently regular. ESA N91-11451# Center for Mathematics and Computer Science, K. Strehmel, W. H. Hundsdorfer, R. Weiner, and A. Arnold (Martin (CWI-NM-R9002; ETN-90-97680) Copyright Avail: NTIS HC/MF A03 Following the method of lines approach, parabolic problems discretized in space by any usual method are discretized in time by the linearly implicit Euler method. To avoid order reduction occurring for problems with time dependent boundary conditions, a modification of the method is proposed. This modified method is proved to be of uniform (independently of the space discretization) order 1 of convergence for wide classes of semilinear and quasilinear problems. ESA N91-11452# Technische Univ., Delft (Netherlands). Faculty of CONNECTED COMPONENTS IN SUPERCRITICAL |