非线性热传导方程的同伦分析解法

The Homotopy Analysis Method for Solving Nonlinear Heat Conduction Equation

本文把同伦分析方法应用于非线性热传导方程的求解,得到了该方程的爆破解并分析了解的性质.把所得同伦近似解与精确解进行了比较,发现两者吻合的很好.此结果表明,同伦分析方法可用于分析非线性偏微分方程的爆破解问题.

The blow-up solution of nonlinear heat conduction equation is obtained by using homotopy analysis method and the property of this solution is analyzed.The comparison is made between homotopy approximate solution and exact solution,and find both agree well.The result indicate that the homotopy analysis method can be used to analysis the blow-up solution of nonlinear partial differential equations.