Differential Equations, Difference Equations and Matrix Theory (Classic Reprint) - Hardcover

Peter Do Lax

9780260661371: Differential Equations, Difference Equations and Matrix Theory (Classic Reprint)

Hardcover

ISBN 10: 0260661376 ISBN 13: 9780260661371

Publisher: Forgotten Books, 2018

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Excerpt from Differential Equations, Difference Equations and Matrix Theory

In section A we apply one of the matrix theorems of section 3 to derive a criterion for the stability of difference schemes used to approximate solutions of differential equations. This criterion is an extension from the symmetric to the nonsymmetric case of Friedrichs' stability theorem for difference equations with positive coefficients. Applications to various specific difference schemes are given at the end of the section.

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About the Author

Peter D. Lax, PhD, is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences at New York University. Dr. Lax is the recipient of the Abel Prize for 2005 "for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions." * A student and then colleague of Richard Courant, Fritz John, and K. O. Friedrichs, he is considered one of the world's leading mathematicians. He has had a long and distinguished career in pure and applied mathematics, and with over fifty years of experience in the field, he has made significant contributions to various areas of research, including integratable systems, fluid dynamics, and solitonic physics, as well as mathematical and scientific computing.

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