Download or read book Numerical Solution of Nonlinear Parabolic Equations written by Samuel Schechter and published by . This book was released on 1977 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method of solution is obtained for a class of nonlinear parabolic partial differential equations. An analysis is made of the existence and uniqueness of a solution to a special class of semilinear systems arising from various discretisations of the differential equation. A numerical procedure for solving singular problems is given. A method of approximate block relaxation is shown to converge globally, and an application to a quadratic system is presented. (Author).
Download or read book Numerical Solution of Nonlinear Parabolic Equations with Axial Symmetry written by Ruslan Hafizovic Farzan and published by . This book was released on 1978 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems written by Jens Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.
Download or read book Numerical Solutions of Three Classes of Nonlinear Parabolic Integro Differential Equations written by T Jangveladze and published by Academic Press. This book was released on 2015-11-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided. Investigations of the described equations include theoretical as well as approximation properties Detailed references enable further independent study Easily understandable proofs describe real-world processes with mathematical rigor
Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Download or read book The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations on the Line written by Thomas Hagstrom and published by . This book was released on 1984 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: The long time behavior of the solutions of nonlinear parabolic initial value problems on the line has been investigated by many authors. In particular they have shown, under certain assumptions, the existence of traveling waves to which a large class of initial data eventually evolves. They have also proved that which traveling wave solution is picked out as the asymptotic state often depends on the behavior of the initial data at infinity. This causes difficulties for the numerical simulation of the long time evolution of such problems. In particular, if an aritificial boundary is introduced, the boundary condition imposed there must depend on the initial data in the discarded region. This work derives such boundary conditions, based on the Laplace transform solution of the linearized problems at + or - infinity. The authors illustrate their utility by presenting a numerical solution of Fisher's equation, a nonlinear parabolic equation with traveling wave solutions which has been proposed as a model in genetics. (Author).
Download or read book Explicit Numerical Solution of Parabolic Differential Equations written by D. W. Burton and published by . This book was released on 1957 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Parabolic Equations and Hyperbolic Parabolic Coupled Systems written by Songmu Zheng and published by CRC Press. This book was released on 2020-05-05 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Download or read book Nonlinear Parabolic Equations written by Lucio Boccardo and published by Longman Publishing Group. This book was released on 1987 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Probability Approach to Numerical Solution of Nonlinear Parabolic Equations written by Grigorij N. Milʹstejn and published by . This book was released on 1997 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Partial Differential Equations written by K. W. Morton and published by Cambridge University Press. This book was released on 2005-04-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.
Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by Academic Press. This book was released on 2014-06-28 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses
Download or read book Time dependent Partial Differential Equations and Their Numerical Solution written by Heinz-Otto Kreiss and published by Birkhäuser. This book was released on 2012-12-06 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.
Download or read book Linear and Nonlinear Parabolic Complex Equations written by Guo Chun Wen and published by World Scientific. This book was released on 1999 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a very interesting book written by a well-known expert on complex methods in partial differential equations. It contains many recent results, many of them published for the first time, some published originally in Chinese".Mathematical Reviews
Download or read book Numerical Solution of Dirichlet Problems for Nonlinear Parabolic Equations by Probability Approach written by Grigorij N. Milʹstejn and published by . This book was released on 1999 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of the Neumann Problem for Nonlinear Parabolic Equations by Probability Approach written by Grigorij N. Milʹstejn and published by . This book was released on 2000 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un
