# Further developments in the noniterative method of solving PDE's in electron scattering

## Description

Abstract Our previous program to solve noniteratively two-dimensional (2D) partial differential equations (PDE's) using a 3-point second-order difference formula is generalized to apply to higher-dimensional PDE's using higher-order difference formulae. This has the effect of generalizing the basic matrix from block tridiagonal to a banded matrix whose width depends on the dimensionally and the difference order desired. The banded matrix is converted to a lower times an upper triangular matrix by a ge... Title of program: SEPDE3 Catalogue Id: ACJB_v1_0 Nature of problem The program will compute a noniterative solution of any two or three dimensional elliptic partial differential equation with rectangular boundary conditions. There are no restrictions on the type of differences used to represent the derivatives or the number of different boundary values that are specified. Coupled equations as well as equations using a higher order than second partial derivative operator, such as the biharmonic operator, also lend themselves to solution using this method. The ma ... Versions of this program held in the CPC repository in Mendeley Data ACJB_v1_0; SEPDE3; 10.1016/0010-4655(92)90017-S This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)