利用显式系数公式高效计算 Laplace 残差幂级数
Efficient Computation of Laplace Residual Power Series with Explicit Coefficient Formulas
AI总结：
针对 RPSM 与 LRPSM 依赖残差分数阶导数或逐次残差误差计算的瓶颈，本文提出直接推导系数显式公式的方法，以提升求解分数阶微分方程的计算效率。
摘要：
残差幂级数法（RPSM）为求解分数阶微分方程提供了一个强大的框架。然而，由于在系数确定过程中必须计算残差函数的分数阶导数，因此产生了显著的计算瓶颈。Laplace 残差幂级数法（LRPSM）通过采用 Laplace 变换在一定程度上解决了这一问题。但它引入了额外的复杂性，并且需要在每次迭代中计算残差误差函数。本工作提出了一种新方法，可直接推导系数的显式公式，从而无需进行迭代残差误差函数计算。与 RPS 方法和 LRPS 方法相比，这一进展显著提高了该方法的计算效率。
英文摘要：
The Residual Power Series Method (RPSM) provides a powerful framework for solving fractional differential equations. However, a significant computational bottleneck arises from the necessity of calculating the fractional derivatives of the residual function within the coefficient determination process. The Laplace Residual Power Series Method (LRPSM) partially addresses this by employing the Laplace transform. However, it introduces additional complexities and requires the computation of the residual error function at each iteration. This work presents a novel approach that directly derives explicit formulas for the coefficients, Bypassing the need for iterative residual error function calculations. This advancement significantly enhances the computational efficiency of the method compared to both RPS method and LRPS method.
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