Accession Number : AD0428251

Title :   AN ITERATIVE TECHNIQUE FOR APPROXIMATING SOLUTIONS TO CERTAIN DIFFERENTIAL EQUATIONS BY TRUNCATED LEGENDRE SERIES,

Corporate Author : TEXAS A AND M UNIV COLLEGE STATION

Personal Author(s) : Heckrotte,Robert Platt

Report Date : JAN 1964

Pagination or Media Count : 54

Abstract : An iterative method for obtaining numerical approximations to solutions of ordinary differential equations is presented. It is, essentially, one developed by Picard. The successive approximations necessary for convergence are in the form of truncated Fourier series of Legendre Polynomials. Certain properties of orthogonal functions are necessary for the development of this study. The method employed and proofs of convergence as well as those numerical techniques that are used in effecting the approximate solution of the differential equations are presented. An explanation is made of the steps necessary to prepare a differential equation for the IBM computer program. Six examples of differential equations solved by the method proposed are given and the numerical results obtained are discussed. The appendix contains a listing of the Fortran computer program which accomplished the numerical portion of this study.

Descriptors :   (*DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), FOURIER ANALYSIS, SERIES(MATHEMATICS), PROGRAMMING (COMPUTERS), PROGRAMMING LANGUAGES, SPECIAL FUNCTIONS (MATHEMATICAL), POLYNOMIALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE