TY - JOUR
T1 - A Well-Conditioned Spectral Integration Method for High-Order Differential Equations with Variable Coefficients
AU - Wang , Yurun
AU - Su , Huiling
AU - Liu , Fei
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1549
EP - 1568
PY - 2024
DA - 2024/10
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0225
UR - https://global-sci.org/intro/article_detail/aamm/23478.html
KW - Spectral integration methods, KdV equation, Kawahara equation.
AB - <p style="text-align: justify;">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.</p>