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Numerical Solution of Boundary Value Problems
Author(s) -
Radok J. R. M.,
Merril R. F.
Publication year - 1960
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19600400503
Subject(s) - boundary value problem , mathematics , bounded function , mathematical analysis , finite difference method , differential equation , finite difference
Many transient physical processes are governed by differential equations which under sufficiently smooth conditions permit the evaluation of higher rates of change of the process variables from their space distributions. An explicit method, utilizing a finite number of such higher rates of change, is examined for the particular problem of one dimensional diffusion in a bounded region with radiation into the adjacent medium. Conditions of high order compatibility between the differential and corresponding difference equations are established and shown to ensure a high order truncation error. Satisfaction of the boundary conditions is achieved by a numerical analogue to the method of images, based on time derivatives of the boundary conditions. Numerical results for four problems are presented.