时间分数阶Swift-Hohenberg方程的一种残差幂级数解法

Residual Power Series Method for Solving the Time-Fractional Swift-Hohenberg Equation

Swift-Hohenberg方程是一个用来描述卷波的Rayleigh-Benard不稳定性的简单模型.利用残差幂级数法求时间分数阶Swift-Hohenberg方程的近似解析解,用该方法求得幂级数展开为五项时方程的解.首先将该方程用幂级数形式表示,然后取前k项,利用残差为0求得其幂级数展开为k项时的近似解析解.通过实验结果的比较,可以得到幂级数的展开项数越多求得的近似解析解越精确,残差幂级数法可以有效地求解时间分数阶Swift-Hohenberg方程的近似解析解.

Swift-Hohenberg equation is a simple model for the Rayleigh-Benard convective instability of roll waves.In this paper,the residual power series method is used to find the approximate analytical solution of time-fractional Swift-Hohenberg equation and obtain the solution when the power series is expanded into five terms.Firstly,the equation is expressed in the form of power series,and then the first k terms is used to obtain the approximate analytical solution according to the residual is zero.By comparing the experimental results,the more the number of expansion terms of the power series can be obtained,the more accurate the solution is.The residual power series method can effectively solve the approximate solution of time-fractional Swift-Hohenberg equation.