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<p>In this paper, we present a co-local method based on shifted Jacobi polynomials to obtain approximate solutions to higher-order differential equations. To develop the desired approach by considering the expansion of the fractional problem solution using Jacobi polynomials and using derivative matrices, the solution of the fractional problem under consideration is transformed into a system of nonlinear algebraic equations. By solving the resulting system and obtaining the unknown expansion coefficients, an approximate solution to the original problem will be obtained. The accuracy of the proposed method was evaluated through various types of tested problems. Numerical results confirm the high accuracy of the proposed method in estimating the solution of the given problems.</p>

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A Computational Method Based on Shifted Jacobi Polynomials for the Fractional Differential Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月12日

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  • S. S. Mirshojaei,
  • E. Shivanian,
  • B. Ghayebi,
  • S. J. Hosseini Ghoncheh

摘要

In this paper, we present a co-local method based on shifted Jacobi polynomials to obtain approximate solutions to higher-order differential equations. To develop the desired approach by considering the expansion of the fractional problem solution using Jacobi polynomials and using derivative matrices, the solution of the fractional problem under consideration is transformed into a system of nonlinear algebraic equations. By solving the resulting system and obtaining the unknown expansion coefficients, an approximate solution to the original problem will be obtained. The accuracy of the proposed method was evaluated through various types of tested problems. Numerical results confirm the high accuracy of the proposed method in estimating the solution of the given problems.