Kernel based meshless approximation of oscillatory Fredholm integral equation

Abstract

In this paper, a numerical meshless solution algorithm for 1D oscillatory Fredholm integral equation is put forward. The proposed algorithm is based on Levin’s quadrature theory incorporating multi-quadric radial basis function (MQ-RBF). The procedure involves local approach of MQ-RBF differentiation matrix. The proposed method is specially designed to handle the case when the kernel function involves stationary point(s). In addition to that the model with free of stationary point(s) is also considered. The main advantage of the meshless procedure is that it can be easily extended to multi-dimensional geometry. These models have numerous physical applications in the field of engineering and physics. The existence of the stationary point(s) in such models has numerous applications in the field of scattering and acoustics etc. (see \cite{zd1D17,JLi12,zd15,Bruno04,HV06}). The proposed meshless method is accurate and cost-effective and provide a trustworthy platform to solve highly oscillatory Fredholm integral equations.