We focus here on a class of fourth-order parabolic equations that can be written as system second-order by introducing an auxiliary variable. design novel fully discrete mixed finite element method to approximate these equations. In our approach, we propose new techniques using the backward differentiation formula for time derivative and special technique approximation nonlinear terms. The use ...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

We propose and analyze a numerical method for solving fourth order differential equations modelling two point boundary value problems. The scheme is based on B-splines collocation. The error analysis is carried out and convergence rates are derived.

This note is inspired by the paper of Bialecki, Fairweather, and Bennett [1] which studies a method for the numerical solution of u00 = f on an interval, and u = f on a rectangle, with zero boundary data; their scheme calculates that C piecewise cubic U for which U 00 (or U) agrees with f at the two (or four) Gauss quadrature points of each subdivision of the original domain. They observe that ...

He’s variational iteration method is applied to fourth-order parabolic partial differential equations with variable coefficients. To illustrate the ability and reliability of the method, some examples are given, revealing its effectiveness and simplicity. c © 2007 Published by Elsevier Ltd

In this paper we present two new schemes, one is third-order and the other is fourth-order. These are improvements of second-order methods for solving nonlinear equations and are based on the method of undetermined coefficients. We show that the fourth-order method is more efficient than the fifth-order method due to Kou et al. [J. Kou, Y. Li, X. Wang, Some modifications of Newton’s method with...