2015•CAUCHY Jurnal Matematika Murni dan AplikasiOpen access

Modified Chebyshev Collocation Method for Solving Differential Equations

Muhammad Arif, Ahmad Kamsyakawuni, Ikhsanul Halikin

Abstract

This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

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Key concepts: Collocation method, Orthogonal collocation, Mathematics, Chebyshev polynomials, Chebyshev nodes, Chebyshev equation, Chebyshev iteration, Collocation (remote sensing)