Convergence analysis of the spectral collocation methods for two-dimensional nonlinear weakly singular Volterra integral equations. (English) Zbl 1391.45005
Summary: We apply Jacobi spectral collocation approximation to a two-dimensional nonlinear weakly singular Volterra integral equation with smooth solutions. Under reasonable assumptions on the nonlinearity, we carry out complete convergence analysis of the numerical approximation in the \(L^\infty\)-norm and weighted \(L^2\)-norm. The provided numerical examples show that the proposed spectral method enjoys spectral accuracy.
MSC:
| 45D05 | Volterra integral equations |
| 65R20 | Numerical methods for integral equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
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