Meshless methods for two-dimensional oscillatory Fredholm integral equations

Abstract In this paper, a meshless solution procedure incorporating delaminating quadrature method for two-dimensional highly oscillatory Fredholm integral equation is put forward. The proposed method is an extension of our earlier findings of meshless methods for two-dimensional oscillatory Fredholm integral equation having kernel function free of stationary phase point(s) (Siraj-ul-Islam et al., 2015). The current method deals not only with the kernels having no stationary phase point(s) but also with the kernels having stationary phase point(s) in the context of highly oscillatory integral equations. The new method is numerically stable and computationally fast. Numerical experiments are presented to testify the robustness and efficiency of the proposed method.

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