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...

In this paper, we develop a new cubic spline method for computing approximate solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation, finite difference and spline methods. Numerical examples a...

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge e...

In this paper, the variational iteration method proposed by Ji-Huan He is applied to solve both linear and nonlinear boundary value problems for fourth order integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the variational iteration method is of high...

Newton’s iteration method is widely used in numerical methods, but its convergence low. Though a higher order algorithm leads to fast convergence, it always complex. An optimal formulation much needed for both and simple calculation. Here, we develop two-step fourth-order iterative based on linear combination of two schemes nonlinear equations, explore the criteria proposed also demonstrate val...