一维Swift-Hohenberg方程定解问题的同伦近似解析解

The Homotopy Approximation Solution of One-dimensional Swift-Hohenberg Equation with Initial and Boundary Conditions

针对一类Swift-Hohenberg方程定解问题,通过选择合适的辅助线性算子,构造出相应的同伦方程,给出了同伦方程的同伦分析解,并对结果进行了分析。与其他方法相比,同伦分析方法在求解非线性问题时有很明显的优势,是一个容易操作并可以控制误差的好方法,为求解强非线性问题开辟了一个全新的途径。

In this paper, in order to solve a class of Swift-Hohenberg equation which has initial-boundary conditions, we had chosen the auxiliary linear operator of homotopy equation, and given the approximation solution and analysis the nature of the solution. The HAM is superior to other methods in solving the nonlinear problems. It is a good way to con- trol error and operate easily. It explores a new way in solving the nonlinear problems.