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Tohidi, Emran; Samadi, O. R. Navid; Shateyi, S.

Convergence analysis of Legendre pseudospectral scheme for solving nonlinear systems of Volterra integral equations. (English) Zbl 1303.65112

Adv. Math. Phys. 2014, Article ID 307907, 12 p. (2014).
Summary: We are concerned with the extension of a Legendre spectral method to the numerical solution of systems of nonlinear 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.

Cited in 4 Documents

MSC:

65R20 Numerical methods for integral equations
45G15 Systems of nonlinear integral equations
45D05 Volterra integral equations
92D25 Population dynamics (general)

Keywords:

Legendre spectral method; systems of nonlinear Volterra integral equations of the second kind; Lotka-Volterra equations; numerical result; convergence
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