Numerical Solution of Partial Differential Equations: Finite Difference Methods

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Clarendon Press, 1985 - Mathematics - 337 pages
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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.
 

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Contents

FINITE
11
ALTERNATIVE
111
The local truncation errors associated with the Pade approxim
124
A comparison of results for methods i ii and iii for
147
HYPERBOLIC EQUATIONS
175
ELLIPTIC EQUATIONS AND SYSTEMATIC
239
Comments on the solution of difference equations covering
257
A worked example covering each method
263
Eigenvalues of the Jacobi and SOR iteration matrices and
275
Theoretical determination of the optimum relaxation parame
282
Introduction to 2cyclic matrices and consistent ordering
288
The ordering vector for a block tridiagonal matrix
294
Stones strongly implicit iterative method
302
A recent direct method
309
INDEX
334
Copyright

A sufficient condition for convergence
269

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About the author (1985)

G. D. Smith is at Brunel University.

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