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Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations, Partial --- 519.6 --- 681.3 *G18 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Numerical analysis --- Numerical solutions --- Numerical solutions. --- Equations aux dérivées partielles --- Solutions numériques --- Differential equations [Partial ] --- Finite differences --- Analyse numérique --- Différences finies --- Analyse numérique. --- Différences finies. --- Numerical analysis. --- Analyse numérique --- Différences finies --- Differential equations, Partial - Numerical solutions --- Equations aux derivees partielles --- Methodes numeriques --- Differences finies

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Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the boo

Difference equations. --- Differential equations, Linear. --- Linear differential equations --- Linear systems --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Equations aux derivees partielles --- Equations aux differences --- Methodes numeriques --- Differences finies

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Equations aux différences --- Numerical solutions of differential equations --- Partial differential equations --- Differential equations, Partial --- Difference equations --- Numerical solutions --- Numerical solutions. --- Equations aux dérivées partielles --- Solutions numériques --- Differential equations, Partial - Numerical solutions --- Difference equations - Numerical solutions --- Equations aux derivees partielles --- Methodes numeriques --- Differences finies

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Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Difference equations --- Differential equations, Partial --- Numerical solutions. --- Numerical solutions of differential equations --- Partial differential equations --- 519.6 --- 681.3 *G18 --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Numerical analysis --- Numerical solutions --- Equations aux dérivées partielles --- Equations aux différences --- Solutions numériques --- Differential equations, Partial - Numerical solutions --- Difference equations - Numerical solutions --- Equations aux derivees partielles --- Methodes numeriques --- Differences finies

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Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.

Differential equations, Partial --- -Finite differences --- 519.6 --- 681.3 *G18 --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Differences, Finite --- Finite difference method --- Numerical analysis --- Partial differential equations --- Numerical solutions --- Finite differences --- Différences finies --- Différences finies --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Numerical solutions of differential equations --- Finite differences. --- Numerical solutions. --- Equations aux dérivées partielles --- Solutions numériques --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Analysis. --- Numerical Analysis. --- Mathematical analysis --- 517.1 Mathematical analysis