Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubi...

A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis o...

We investigate the possibility of applying approximation methods to the famous Muskhelishvili equation on a simple closed smooth curve Γ. Since the corresponding integral operator is not invertible the initial equation has to be corrected in a special way. It is shown that the spline Galerkin, spline collocation and spline qualocation methods for the corrected equation are stable, and the corre...

An Efficient Algorithm Based on Quadratic Spline Collocation and Finite Difference Methods for Parabolic Partial Differential Equations Tong Chen Master of Science Graduate Department of Computer Science University of Toronto 2005 An efficient algorithm which combines quadratic spline collocation methods (QSC) for the space discretization and classical finite difference methods (FDMs), such as ...