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Manuscript Title: A non-iterative method for solving PDE's arising in electron scattering.
Authors: E.C. Sullivan, A. Temkin
Program title: SEPDE
Catalogue identifier: AANP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)97
Programming language: Fortran.
Computer: IBM 360/91.
Operating system: HASP/OS MVT.
RAM: 125K words
Word size: 32
Peripherals: disc.
Keywords: Atomic physics, Electron, Scattering, Schrodinger equation, Electron-atom scattering, Electron-molecule, Partial differential Equations, Non-iterative block Solution, Large linear systems, Coupled elliptic Partial differential Equations, Rectangular boundary Conditions, Non-iterative partial Differential equation Method.
Classification: 2.4.

Nature of problem:
The major approach to (low energy) scattering of electrons from atomic and, more recently, molecular systems comes from decomposing the scattering wave function into partial waves. Rather than expand the solutions of the partial wave equations to obtain a coupled set of ordinary integro-differential equations, the SEPDE program solves the partial wave equations directly, avoiding the convergence problems encountered with arbitrarily truncating the expansion of each specific partial wave equation.

Solution method:
The partial differential equation is approximated by a linear system of equations. The system of equations is arranged in a block tridiagonal form and the solution of the system obtained directly rather than iteratively. Since the method of solution uses matrices dimensioned according to the block size, one avoids the requirement of banded methods that coefficients of the matrix within the band be in the computer memory at the same time.

The program is restricted to two-dimensional elliptic partial differential equations for rectangular regions. The program will handle mutliple boundary conditions and systems of coupled equations. The computer memory requirements depend on the grid size chosen and the number of equations to be solved. The dimensioning for a given problem is done in one BLOCK DATA initializing routine. The user must also provide a subroutine which evaluates the coefficients of the block diagonal matrices; analogous to the way a derivative routine must be provided for routines which solve systems of ordinary differential equations.