Title: A second order implicit-explicit general linear method based on continuous interpolants

Authors: Sakshi Gautam; Ram K. Pandey

Addresses: Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya (A Central University), Sagar, PIN – 470003, Madhya Pradesh, India ' Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya (A Central University), Sagar, PIN – 470003, Madhya Pradesh, India

Abstract: Implicit-explicit (IMEX) general linear method (GLM) is a special class of GLM that solves differential systems containing both non-stiff and stiff parts. In the present paper, we present the continuous extension of an IMEX GLM of order two and stage order two. We derive the governing order conditions for IMEX-GLM using continuous interpolants. The proposed scheme is constructed using the continuous extension of the explicit counterpart of IMEX-GLM. Numerical examples of three partitioned (containing both the non-stiff and stiff parts) systems of problems in differential equations have been given to demonstrate the effectiveness of the second-order IMEX GLM based on continuous interpolants. The reported results reveal a good agreement between the reference solution and the numerical solution, and no order reduction is noticed for the proposed second-order method. Also, CPU time in seconds is calculated and reported in tables, which reflect the cost efficiency of the proposed scheme.

Keywords: implicit-explicit solver; general linear method; GLM; continuous extension; order conditions; time-dependent partitioned nonlinear differential equations.

DOI: 10.1504/IJANS.2025.151206

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.2, pp.195 - 215

Received: 12 Oct 2024
Accepted: 16 Dec 2024
Published online: 19 Jan 2026 *

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