A Spectral Approach to Solve High-Order Ordinary Differential Equations: Improved Operational Matrices for Exponential Jacobi Functions

Hany Mostafa Ahmed ()
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Hany Mostafa Ahmed: Department of Mathematics, Faculty of Technology and Education, Helwan University, Cairo 11281, Egypt

Mathematics, 2025, vol. 13, issue 19, 1-19

Abstract: This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of this approach is using the spectral collocation method (SCM) and building operational matrices (OMs) for the ordinary derivatives (ODs) of GEJFs. These lead to efficient and accurate computations. The suggested algorithm’s convergence and error analysis is proved. We present numerical examples to demonstrate the applicability of the approach.

Keywords: Jacobi polynomials; exponential Jacobi functions; differential equations; collocation method; initial value problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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