Comparative Analysis of Polynomials with Their Computational Costs

Qasim Khan; Anthony Suen

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arXiv · 2411.00487

Comparative Analysis of Polynomials with Their Computational Costs

Qasim Khan·Anthony Suen

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Abstract

In this article, we explore the effectiveness of two polynomial methods in solving non-linear time and space fractional partial differential equations. We first outline the general methodology and then apply it to five distinct experiments. The proposed method, noted for its simplicity, demonstrates a high degree of accuracy. Comparative analysis with existing techniques reveals that our approach yields more precise solutions. The results, presented through graphs and tables, indicate that He's and Daftardar-Jafari polynomials significantly enhance accuracy. Additionally, we provide an in-depth discussion on the computational costs associated with these polynomials. Due to its straightforward implementation, the proposed method can be extended for application to a broader range of problems.

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Qasim Khan, Anthony Suen. 2024-11-01. Comparative Analysis of Polynomials with Their Computational Costs. https://arxiv.org/abs/2411.00487

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