A Well-Conditioned Spectral Integration Method for High-Order Differential Equations with Variable Coefficients
Year: 2024
Author: Yurun Wang, Huiling Su, Fei Liu
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1549–1568
Abstract
A well-conditioned spectral integration (SI) method is introduced, developed and applied to $n$th-order differential equations with variable coefficients and general boundary conditions. The approach is based on integral reformulation techniques which lead to almost banded linear matrices, and the main system to be solved is further banded by utilizing a Schur complement approach. Numerical experiments indicate the spectral integration method can solve high order equations efficiently, oscillatory problems accurately and is adaptable to large systems. Applications in Korteweg-de Vries (KdV) type and Kawahara equations are carried out to illustrate the proposed method is effective to complicated mathematical models.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0225
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1549–1568
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Spectral integration methods KdV equation Kawahara equation.