摘要
应用同伦分析法研究一类非线性偏微分方程的解析近似解问题。通过选取合适的线性辅助算子和初始值,引入适当的辅助参数和辅助函数来调节、控制级数解的收敛区域与收敛速度,即可求得一类非线性偏微分方程的解析近似解。该方法为非线性偏微分方程的求解开辟了一个全新的途径。
An analytical approximate solution for a class of nonlinear partial differential equations was obtained by the Homotopy Analysis Method （HAM） in this paper. Different from other approximate solutions, the HAM provides us with a great freedom to choose basis functions, so that a nonlinear problem can be more effectively approximated. Regulating and controlling the convergence region and convergence rate of the series solution by introducing auxiliary parameters and functions, the HAM opens up a new approach of solutions of nonlinear partial differential equations.
出处
《农业科技与装备》
2014年第5期44-46,49,共4页
Agricultural Science & Technology and Equipment
关键词
非线性
偏微分方程
同伦分析法
解析近似解
nonlinear
partial differential equation
homotopy analysis method
approximate analytical solution
