同伦分析方法求具有边界条件的扩散方程的精确解

关于如何求解具有边界条件的扩散方程的数值解,给出了一种新的方法——同伦分析方法(HAM)。在此方法中给出一族级数解, 其递推关系很明显,在原问题边界和初始条件约束下级数解的初始近似值可以任意选取。因为同伦分析方法含有辅助参数h, 这为调节和控制级数解的收敛区域提供了一个简单有效的方法。把同伦分析方法得到的结果与精确解和其他方法得到的结果做了比较, 结果表明同伦分析方法非常简单有效。

On the exact solution of a diffusion equation with boundary conditions by the homotopy analysis method

The homotopy analysis method was presented(short: HAM) for obtaining numerical solutions of a diffusion equation with boundary conditions.The series solution was developed and the recurrence relations were explicitly given.The initial approximation can be freely chosen with possible unknown constants,which can be determined by imposing the boundary and initial conditions.The HAM contains the auxiliary parameter h,which can provide a simple way to adjust and control the convergence region of solution series.Comparisons were made between the HAM,the exact solution and the other method.The results revealed that the HAM is effective and simple.