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2015•LMS Journal of Computation and MathematicsOpen access

Piecewise Legendre spectral-collocation method for Volterra integro-differential equations

Zhendong Gu, Yanping Chen

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Abstract

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in $h^{m}N^{-m}$ -version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

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What this paper is about

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in $h^{m}N^{-m}$ -version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

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Available abstract

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in $h^{m}N^{-m}$ -version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

Key concepts: Legendre polynomials, Piecewise, Mathematics, Collocation (remote sensing), Collocation method, Orthogonal collocation, Volterra integral equation, Spectral method

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