An Alternating Group Explicit Iterative Method for Solving Four-order Parabolic Equations

A class of alternating group explicit iterative method using the C-N scheme is derived for solving four order parabolic equations, and the analysis for convergency is given. In the end, the numerical result is given, which shows the iterative method is convergent, high precision, and is suitable for parallel computing. 1 Preface In Science and engineering computing, parabolic equations are important partial differential equations. many researches on numerical algorithms for low order parabolic equations have been done so far, but schemes for high order parabolic equations which are of high precision and are of constant stability have been scarcely presented. With the development of parallel computer, researches on parallel computing method is getting more and more popular, In [1], Evans D J presented a class of alternating group method(AGE), which is constantly stable and is suitable for parallel computing. Later, The method is widely cared, and many alternating group schemes for kinds of partial differential equations are presented in [2-6] and [7, 9, 10]. In this thesis, an alternating group explicit iterative method using the C-N scheme is derived for solving four-order parabolic equations. The result of convergence analysis for the iterative method shows that the method is convergent. In the end, results of numerical experiments are given, which shows that the method is of high precision. In this thesis, a time-dependent periodic boundary problem of four order parabolic equation (1) is considered.