Meshless methods for multivariate highly oscillatory Fredholm integral equations

In this paper, accurate and efficient algorithms based on global and local meshless formulations with modified Levin׳s quadrature are proposed for numerical solution of two-dimensional highly oscillatory Fredholm integral equations. The main focus of the study is to extend applications of global and local meshless procedures to integral equations on uniform as well as irregular nodes. This work will also focus on undertaking a comparative performance of the global and local meshless methods. The proposed methods will be tested on different test problems having phase function free of stationary points. From the numerical results we will draw some conclusions about accuracy and robustness of the proposed approaches. Further, the computational cost and the singularity of the system matrices in terms of condition number of both the local and global meshless methods will be investigated. A comprehensive analysis will ultimately establish computational efficiency and accuracy of the local approach.