A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions
In this paper, an effective numerical method for solving nonlinear Volterra partial integro-differential equations is proposed. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function which is the memory of problem. This method is based on radial basis functions (RBFs) and finite difference method (FDM) which provide the approximate solution. These techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some illustrative examples are shown to describe the method. Numerical examples confirm the validity and efficiency of the presented method.
parabolic-type volterra partial integro-differential equations radial basis functions finite difference method generalized thin plate splines composite trapezoidal integration method