R70-6 Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems
Issue No. 05 - May (1970 vol. 19)
W.J. Karplus , University of California
The purpose of this paper is to provide a broad review of a class of unconventional computational methods for solving certain partial differential equations. The most widely used analog and digital techniques for solving initial-value problems involve the discretization of the space domain, with the aid of finite difference approximations. In the case of digital methods, there results a set of algebraic equations which must be solved for each step in the time domain. In analog techniques, finite difference approximations lead to a set of simultaneous ordinary differential equations, one for each grid point in this space domain. These equations can then be integrated using analog integrators. Although quite general in their applicability, finite differences methods often entail excessive and uneconomical computational efforts. This shortcoming, as well as the desire to explore new potential applications for hybrid computers, has led a number of investigators to experiment with alternative techniques, techniques which the author of the paper under review has chosen to classify as functional approximation methods.
W. Karplus, "R70-6 Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems," in IEEE Transactions on Computers, vol. 19, no. , pp. 465, 1970.