DTM-Adomian-pade求解非线性分数阶微分方程

DTM-Adomian-pade for solving nonlinear fractional differential equations

为求解R-L定义下的分数阶非线性微分方程近似解析解,将Adomian多项式、Padé逼近法与R-L微分变换法相结合,提出改进的广义微分变换法。利用Adomian多项式代替方程中的非线性部分,对方程进行广义微分变换法求出其级数解,运用Pade法对其级数解进行逼近。改进的微分变换法不仅计算简单,具有较小的计算量,而且扩大了级数解得收敛范围,具有较高的精度。最后给出数值算例,验证了算法的有效性,为计算R-L分数阶非线性微分方程提出新的计算格式。

An improved generalized differential transformation method is proposed for solving the approximate analytical solution of nonlinear fractional differential equation in the definition of R-L. The method is a combination with differential transformation,Adomian polynomial,Padé approximation. The method is not only simple and has little calculation,but also has higher accuracy. Finally,numerical example is given to verify the effectiveness of the algorithm,which proposes a new calculating scheme for nonlinear fractional differential equations.