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The method of moments and its optimization
Author(s) -
Leventhal Stephen H.
Publication year - 1975
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620090206
Subject(s) - mathematics , piecewise , partial differential equation , boundary value problem , finite element method , moment (physics) , mathematical analysis , ordinary differential equation , numerical partial differential equations , numerical analysis , function (biology) , differential equation , physics , classical mechanics , evolutionary biology , biology , thermodynamics
The method of moments is a semidiscrete numerical method for solving partial differential equations. The method approximates the solution of a partial differential equation by a finite sum of products of two functions. One function in the product is an unknown function of a single variable and the other function (moment function) is a prescribed function in the remaining variables. Using variational technique we obtain a finite system of boundary value problems of ordinary differential equations for the unknown functions. The main goal of this paper is the study of the theoretical background and numerical effectiveness of the method of moments for solving linear partial differential equations on rectangular‐like domains. The mathematical formulation of the method together with error estimates and the theory of optimal moment functions are given. If for the one‐dimensional moment functions piecewise polynomials of degree K are used then finite element type error bounds are obtained for the approximate solution in two dimensions. We also consider the numerical implementation of the method through the factorization method and efficient initial value methods. Several numerical examples showing the efficiency of the method are presented.