Walsh関数系を用いた2点境界値問題の数値解法

概要

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An approximate method for numerical solution is considered for the boundary-value problems of linear ordinary differential equations of second order in the form L(y)=y"-q(x)y=r(x), with y(a)=α,y(b)=β. First, y is expanded in a finite series of Walsh functions wal(j-1,x)with unknown coefficients c_j,such that y=?^^n__<j=1>c_jwal(j-1,x). Then, c_j can be determined by the ordinary method of weighted residuals with weight functions of wal(i-1,x). This method is equivalently transformed into a simpler method without any loss of accuracy. That is, y is expanded as y=?^^n__<j=1>c_jf_j(x), where f_j are characteristic functions determined by [numetical formula] with D_j=(x_j-h/2,x_j+h/2), h=(b-a)/n,x_j=a+(j-1/2)h. The method requires merely the collocation to obtain the unknown coefficients c_j.
一般社団法人情報処理学会の論文
1978-06-15