修正局部Crank-Nicolson法对于二维热传导方程的应用

1．关于一线热传导方程解法的描述考虑一维空间的热传导方程的数值解法，这里Q＝（0，1）．对于（1．1）的微分项用中心差商代替，就得到半差分方程式。（；，O的近似解，并且A是三对角矩阵古典显格式、隐格式和Crank－Nicolson法可以表示为从这些近似式可以看出，为能得到未来的近似解法，应该考虑exP（兴A）的近似式．只要推—“————一’—’—”“—”—－’””’”“‘”—“”’～’””“——‘””’””一’———”“”－－””h‘”一’—‘—”—”””—”一出exP（兴川的新近似式，就能得到新的近似解法．因此以下给…

A CORRECTOR LOCAL C-N METHOD FOR THE TWO-DIMENSIONAL HEAT EQUATION

This paper describes a numerical method for solving initial-boundary value problems of parabolic equations. Based on a representation of the Trotter product,we derive a new technigue for two-dimensional problems, which does not yield a large linear system, by using a splitting of the coefficient matrix. Furthermore,we prove that the proposed method, which is explicit, and unconditionally stable.Some numerical examples show that our method is superior to the Crank-Nicolson method.