A higher accuracy finite difference method for an elliptic equation of order four

MSNFD : A Higher Order Finite Difference Method for Solving Elliptic PDEs on scattered

This paper presents a method of producing higher order discretization weights for linear differential and integral operators using the Minimum Sobolev Norm idea[1][2] in arbitraty geometry and grid configurations. The weight computation involves solving a severely ill-conditioned weighted least-squares system. A method of solving this system to very high-accuracy is also presented, based on the...

Fourth-order finite difference method for solving Burgers' equation

In this paper, we present fourth-order finite difference method for solving nonlinear one-dimensional Burgers equation. This method is unconditionally stable. The convergence analysis of the present method is studied and an upper bound for the error is derived. Numerical comparisons are made with most of the existing numerical methods for solving this equation. 2005 Elsevier Inc. All rights res...

On a Higher-Order Nonlinear Difference Equation

and Applied Analysis 3 After k steps we obtain the following formula xn A ⎛ ⎝ A x r/p n−k ⎛ ⎝ A x r/p2 n−k x r/p n−k−1 ⎛ ⎝ A x r/p3 n−k x r/p2 n−k−1x r/p n−k−2

On a Higher-Order Difference Equation

A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...