On the Partial Difference Equations, of Mathematical Physics (Classic Reprint) - Hardcover

Richard Courant

9780265500422: On the Partial Difference Equations, of Mathematical Physics (Classic Reprint)

Hardcover

ISBN 10: 0265500427 ISBN 13: 9780265500422

Publisher: Forgotten Books, 2018

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Turn differential equations into workable difference problems on a grid—and learn how the solutions behave as the mesh tightens.

This elementary study shows how to replace small changes with difference quotients on a rectilinear mesh, and what that implies for solving the core equations of mathematical physics. The authors illuminate the path from discrete models to the continuous world of partial differential equations.

This edition focuses on the elliptic and hyperbolic cases, presenting boundary value and eigenvalue problems alongside practical examples. It explains Green's formula in the difference setting, and discusses when and how the grid-based solutions converge to the familiar differential equation solutions. The text also connects these ideas to potential theory, the random walk, and related topics, offering a clear route from algebraic steps to analytic outcomes.

See how difference expressions are built from forward and backward quotients
Learn about convergence properties as the mesh width goes to zero
Explore boundary value, eigenvalue, and initial-value problems in a discrete framework
Understand the role of Green’s formula and adjoint expressions in this context

Ideal for readers of applied mathematics, mathematical physics, and numerical methods who want a solid, accessible foundation in turning differential problems into difference problems on a grid.

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