Efficient Method for Solving Fourth Order PDEs

Fourth-Order Time-Stepping for Stiff PDEs

A modification of the exponential time-differencing fourth-order Runge–Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competi...

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

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...

Cubic splines method for solving fourth-order obstacle problems

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...

Traveling Wave Solutions of Fourth Order PDEs for Image Processing