Innovative Solutions for the Kadomtsev–Petviashvili Equation via the New Iterative Method

4区工程技术 Q1 Mathematics Mathematical Problems in Engineering Pub Date : 2024-01-16 DOI:10.1155/2024/5541845

Belal Batiha

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Abstract

This research paper presents a new iterative method (NIM) for obtaining the solution to the potential Kadomtsev–Petviashvili (PKP) equation. NIM is a promising approach to solving complex mathematical problems, and its effectiveness and efficiency are highlighted through its application to the PKP equation. The results obtained through the use of NIM are compared to the exact solutions of the PKP equation, and it is found that the NIM approach provides results that are in close agreement with the exact solutions. This demonstrates the utility and accuracy of NIM and makes it a valuable tool for solving similar mathematical problems in the future. Furthermore, the lack of discretization in the NIM approach makes it a more convenient method for solving the PKP equation compared to traditional approaches that require discretization. Overall, the findings of this research paper suggest that NIM is a highly effective and convenient method for obtaining approximate analytical solutions to complex mathematical problems, such as the -dimensional PKP equation.

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通过新迭代法解决卡多姆采夫-彼得维亚什维利方程的创新方案

本研究论文介绍了一种新的迭代法（NIM），用于获得潜在的卡多姆采夫-彼得维亚什维利（PKP）方程的解。NIM 是解决复杂数学问题的一种有前途的方法，它在 PKP 方程中的应用凸显了其有效性和效率。通过将使用 NIM 所获得的结果与 PKP 方程的精确解进行比较，发现 NIM 方法所提供的结果与精确解非常接近。这证明了 NIM 的实用性和准确性，使其成为今后解决类似数学问题的重要工具。此外，与需要离散化的传统方法相比，NIM 方法不需要离散化，因此是一种更方便的 PKP 方程求解方法。总之，本文的研究结果表明，NIM 是一种高效便捷的方法，可用于获得复杂数学问题（如-维 PKP 方程）的近似解析解。

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来源期刊

Mathematical Problems in Engineering 工程技术-工程：综合

CiteScore

4.00

自引率

0.00%

发文量

2853

审稿时长

4.2 months

期刊介绍： Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.