Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations | Zendy

Emran Tohidi | Zendy; O. R. Navid Samadi | Zendy; Stanford Shateyi | Zendy

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Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations

Author(s) -

Emran Tohidi,

O. R. Navid Samadi,

Stanford Shateyi

Publication year - 2014

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2014/307907

Subject(s) - legendre polynomials , mathematics , volterra integral equation , convergence (economics) , nonlinear system , rate of convergence , exponential function , integral equation , pseudospectral optimal control , scheme (mathematics) , mathematical analysis , pseudo spectral method , computer science , fourier transform , computer network , physics , quantum mechanics , economics , economic growth , channel (broadcasting) , fourier analysis

We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence

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