Alternating direction scheme for a kind of nonlinear evolution equation
A class of nonlinear evolution equations are presented in this paper. By transforming and adding a perturbation term, we have got a different scheme of operator times type. In this paper we first get a alternating direction difference of new Douglus type of scheme through operator splitting method then solve the problem by alternating direction method, this yields that the multidimensional difference system are decomposed to a set of independent one-dimensional problems, consequently calculation efficiency is greatly improved. It is shown in this paper that the scheme is second-order accurate in time and in space in the H1-norm, and optimal order error estimates in L2 is obtained by the calculation of vector product and the use of theory and technique of priori estimate. Numerical results validate the theoretical analysis and the efficiency of this scheme.
Author's Name: Su, Z., Nashun, B.
Volume: Volume 1
Issues: Issue 1
Keywords: Alternating direction scheme, Error estimation, Nonlinear evolution equations