Journals
Resources
About Us
Open Access

A Well-Conditioned Spectral Integration Method for High-Order Differential Equations with Variable Coefficients

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Yurun Wang

Huiling Su

Fei Liu