‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

‎In this paper‎, ‎an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations‎. ‎The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎Under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎Numerical results on some problems are given...

In this paper, a numerical method is proposed to approximate the numeric solutions of nonlinear Fisher's reaction– diffusion equation with modified cubic B-spline collocation method. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply modified cu...

In this paper, a highly accurate method is introduced to achieve the numerical solution of advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in spatial-domain discretization and Adams Moulton scheme temporal-domain discretization. Two test problems are studied validate effectiveness new presented efficiency approximate results tes...