Smith G.D. Numerical Solution of Partial Differential Equations: Finite Difference Methods

3rd ed. — Oxford University Press, 1986. — 350 p. — (Oxford Applied Mathematics and Computing Science). — ISBN 0198596502, 9780198596509.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.