A NEW LEGENDRE POLYNOMIAL-BASED APPROACH FOR NON-AUTONOMOUS LINEAR ODES

被引：0

作者：

Pozza S. ^{[1
]}

van Buggenhout N. ^{[2
]}

机构：

[1] Department of Numerical Mathematics, Charles University, Sokolovská 83, Praha 8

[2] Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés

来源：

Electronic Transactions on Numerical Analysis | 2024年 / 60卷

关键词：

Legendre polynomials; ordinary differential equations; spectral accuracy;

D O I：

10.1553/etna_vol60s292

中图分类号：

学科分类号：

摘要：

We introduce a new method with spectral accuracy to solve linear non-autonomous ordinary differential equations (ODEs) of the kind dtd ũ(t) = f̃(t)ũ(t), ũ(−1) = 1, with f̃(t) an analytic function. The method is based on a new analytical expression for the solution ũ(t) given in terms of a convolution-like operation, the ?-product. We prove that, by representing this expression in a finite Legendre polynomial basis, the solution ũ(t) can be found by solving a matrix problem involving the Fourier coefficients of f̃(t). An efficient procedure is proposed to approximate the Legendre coefficients of ũ(t), and the truncation error and convergence are analyzed. We show the effectiveness of the proposed procedure through numerical experiments. Our approach allows for a generalization of the method to solve systems of linear ODEs. © 2024, Kent State University.

引用

页码：292 / 326

页数：34

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