ON AN ANALOGUE OF THE EULER-CAUCHY POLYGON METHOD FOR THE PARTIAL DIFFERENTIAL EQUATION UXL...XN EQUALS F
Abstract
This paper gives constructive proofs of existence theorems for two cases of the partial differential equation u sub x1...sub xn equals f where f is a function of x sub 1,...,x sub n, u and the pure mixed partial derivatives of u up through order n-1. The method used is an analogue of the Euler-Cauchy polygon method and yields a numerically feasible procedure for constructing solutions. Two inequalities of independent interest are proved as lemmata for the existence proofs, and the properties of an interesting class of interpolatory functions are obtained. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 20, 1961
- Accession Number
- AD0258670
Entities
People
- Irving Gluck
Organizations
- Naval Ordnance Laboratory