10.1007/s40096-021-00448-8

Some computational convergent iterative algorithms to solve nonlinear problems

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  • Mohsen Rabbani*1,
  • Ji Huan He2,
  • Murat Düz3,
  1. Department of Applied Mathematics, Sari Branch, Islamic Azad University, Sari, IR
  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, CN School of Science, Xi’an University of Architecture and Technology, Xi’an, CN National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, CN
  3. Faculty of Sciences Department of Mathematics, Karabuk University, Karabük, TR

Published in Issue 2021-11-30

How to Cite

Rabbani, M., He, J. H., & Düz, M. (2021). Some computational convergent iterative algorithms to solve nonlinear problems. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00448-8
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Abstract

Abstract In this article, we apply Fourier transform to convert a nonlinear problem to a suitable equation and then we introduce a modified homotopy perturbation to divide the above equation into some smaller and easier equations. These equations can be solved by some iterative algorithms which are constructed by modified homotopy perturbation and Adomian polynomials. As an example, we use the iterative algorithms to find the exact solution of nonlinear ordinary and partial differential equations (in abbreviated form, ODE and PDE). To show ability and validity of the presented algorithms, we solve Korteweg–de Vries ( KdV ) equation to approximate the exact solution with a high accuracy. Furthermore, a discussion is presented herein about the convergence of the proposed algorithms in Banach space

Keywords

  • Iterative algorithms,
  • Modified homotopy,
  • Adomian polynomials,
  • Ordinary differential equations (ODE),
  • Partial differential equations (PDE),
  • KdV equation

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