Universal Coefficients Formula for the Residual Power Series Method with General Integral Transform
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909241402458112 |
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| author | Kittipoom, Pisamai |
| author_facet | Kittipoom, Pisamai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Coefficients Formula for the Residual Power Series Method with General Integral Transform Kittipoom, Pisamai General Mathematics 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. |
| title | Universal Coefficients Formula for the Residual Power Series Method with General Integral Transform |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2407.03326 |