On graded meshes for weakly singular Volterra integral equations with oscillatory trigonometric kernels

• Autores: Qinghua Wu
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 263, Nº 1, 2014, págs. 370-376
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.12.039
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• Resumen

  • We compare the collocation methods on graded meshes with that on uniform meshes for the solution of the weakly singular Volterra integral equation of the second kind with oscillatory trigonometric kernels. Due to, in general, unbounded derivatives at the left endpoint of the interval of integration, we should approximate the solution of the integral equation by collocation methods on graded meshes. However, we show that this nonsmooth behavior of the solution has little effect on the approximate solution when the kernels of integral equation are highly oscillatory. Numerical examples are given to confirm the proposed results.