Convergence analysis of spectral methods for high-order nonlinear Volterra integro-differential equations. (English) Zbl 1438.65343
Summary: In this paper, we propose and analyze Chebyshev spectral collocation approximation for high-order nonlinear Volterra integro-differential equations. Under reasonable assumptions on the nonlinearity, it is shown that this numerical method converges exponentially in both \(L^\infty \)-norm and \(L^2\)-norm. Numerical results of several test examples are presented and comparisons are made with some existing numerical methods to prove the superiority and the effectiveness of the proposed method.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45D05 | Volterra integral equations |
| 45J05 | Integro-ordinary differential equations |
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