Partial Differential and Difference Equations

Author: Arnoff, E. Leonard

Year: 1952

Degree: Dissertation (Ph.D.)

Advisor: Bohnenblust, Henri Frederic

Committee Member: Unknown, Unknown

Option: Mathematics; Physics

DOI: 10.7907/PS1G-NW89

Abstract

In this thesis, general conditions on the coefficients of difference equations are obtained which insure the convergence of solutions of these difference equations to the solutions of the corresponding partial differential equations. A general method which is applicable to a wide variety of partial differential equations is presented here. However, in order to simplify the presentation of this method and to leave out calculations which are not essential to the description of the method, the discussion is centered about the partial differential equations

əu/əy = c əu/əx and ə²u/əx² = ə²u/əy².

The treatment of these simpler problems then serves to indicate the method for more general problems.

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