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Collocation methods for nonlinear Volterra integral equations with oscillatory kernel
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DOI：10.1016/j.apnum.2024.05.002.png)
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Abstract
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This work is devoted to the numerical solution of second kind nonlinear Volterra integral equations with highly oscillatory kernel. We use a collocation approach by discretizing the oscillatory integrals in the collocation equation using a Filon-type quadrature rule. We investigate the convergence of the numerical method in terms of step length h and frequency omega. As h decreases, the suggested technique converges with order d, while its asymptotic order as the frequency increase, is at least 1 and may reach 2 in some cases. Numerical experiments validate theoretical results.
Keywords:
Nonlinear Volterra integral equations
Highly oscillatory kernel
Collocation methods
Convergence analysis
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