A Well-Conditioned Spectral Integration Method for High-Order Differential Equations with Variable Coefficients (Advances in Applied Mathematics and Mechanics, 2024)
A well-conditioned spectral integration (SI) method is introduced, developed and applied to $n$th-order differential equations with variable coefficients andgeneral boundary conditions. The approach is based on integral reformulation techniques which lead to almost banded linear matrices, and the main system to be solvedis further banded by utilizing a Schur complement approach. Numerical experimentsindicate the spectral integration method can solve high order equations efficiently,oscillatory problems accurately and is adaptable to large systems. Applications inKorteweg-de Vries (KdV) type and Kawahara equations are carried out to illustratethe proposed method is effective to complicated mathematical models.