Numerical simulation of nonlinear parabolic type Volterra partial integro-differential equations using quartic B-spline collocation method

Abstract

A quartic B-spline collocation method is proposed for numerical solution of nonlinear parabolic type Volterra partial integro-differential equations. The scheme is developed by discretization of the time derivative using centeral difference formula while the spatial derivatives are approximated using quartic B-spline functions. The integral term is approximated by composite trapezoidal rule. Numerical solution of five test problems are provided to validate the scheme. Accuracy of the method is assessed in terms of various error norms. The results are thoroughly compared with radial basis functions collocation method.