Universal Coefficients Formula for the Residual Power Series Method with General Integral Transform

2024/05/04 by Kittipoom, Pisamai
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2407.03326

Abstract

This paper introduces a novel approach to address inherent limitations in the Residual Power Series (RPS) method and its variants with Laplace-like transforms when applied to solving time-fractional differential equations. Existing methods, while successful, often require computationally expensive calculations for the coefficients of the series solution. To overcome this limitation, we propose a new framework for the RPS method that utilizes a general integral transform. This framework incorporates an explicit formula for calculating coefficients, thereby eliminating repetitive computations and streamlining the solution process. Moreover, it offers a universally applicable approach, remaining compatible with various RPS methods that employ Laplace-like transform variants.

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