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arXiv · 2608.23494

Numerical Solution of Pantograph Delay Integrodifferential Equation of Volterra Type: Collocation Method Based on Shifted Jacobi Polynomials

Richard Olu Awonusika·Olasupo John Felemu·Olawale Olaonipekun Ajijola·Yoyinade Joose Aborisade
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Abstract

Pantograph arises in electric trains, material modelling, and the modelling of quantum dot lasers. Pantograph integrodifferential equations are integrodifferential equations involving proportional delays; and they appear in fields such as electrodynamics, epidemiology, control theory, astrophysics, economics, and engineering. This research presents an efficient collocation method based on shifted Jacobi polynomials for obtaining numerical solutions of a class of first order pantograph delay integrodifferential equation of Volterra type with an initial condition. The proposed method expresses the solution of the governing equation as a shifted Jacobi polynomial series with expansion coefficients which are to be determined. Collocating at the roots of the shifted Jacobi polynomials, the underlying problem is reduced to a system of algebraic equations in the unknown expansion coefficients of the shifted Jacobi polynomial series solution. Newton's method is subsequently used to solve the resulting system of algebraic equations and numerical values of the expansion coefficients are obtained. The obtained coefficients are substituted into the assumed series solution to obtain the required numerical solutions. The applicability, reliability, efficiency, and accuracy of the shifted Jacobi collocation method are demonstrated through illustrative examples. Results obtained using the proposed method are compared with exact solutions and other published results. Comparisons of errors which are presented in tables reveal that our method approximates the solution better than the methods under comparison.

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Richard Olu Awonusika, Olasupo John Felemu, Olawale Olaonipekun Ajijola, Yoyinade Joose Aborisade. 2026-08-24. Numerical Solution of Pantograph Delay Integrodifferential Equation of Volterra Type: Collocation Method Based on Shifted Jacobi Polynomials. https://arxiv.org/abs/2608.23494

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