High Order Continuous Extended Linear Multistep Methods for Approximating System of ODEs

Abstract

A class of high-order continuous extended linear multistep methods (HOCELMs) is proposed for solving systems of ordinary differential equations (ODEs). These continuous schemes are obtained through multistep collocation at various points to create a single block method with higher dimensions. This class of schemes consists of A-stable methods with a maximum order of $p\leq14$, capable of yielding moderately accurate results for equations with several eigenvalues of the Jacobians located close to the imaginary axis. The results obtained from numerical experiments indicate that these schemes show great promise and competitiveness when compared to existing methods in the literature.