RBF Based Localized Method for Solving Nonlinear Partial Integro-Differential Equations

In this work, a numerical scheme is constructed for solving nonlinear parabolic-type partial-integro differential equations. The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes. The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule. The resultant differentiation matrices are sparse in nature. After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs. Then ODEs system can be solved by various types of ODE solvers. The proposed numerical scheme is tested and compared with other methods available in literature for different test problems. The stability and convergence of the present numerical scheme are discussed.