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A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem

Author

Listed:
  • Azarnavid, Babak
  • Emamjomeh, Mahdi
  • Nabati, Mohammad

Abstract

An iterative shooting-like method based on the shifted Chebyshev polynomials is proposed for solving the nonlinear fractional boundary value problems with the multi-point boundary conditions. The proposed method can be applied easily to various nonlocal linear boundary conditions. Here, we investigate the convergence of the proposed method for the nonlinear problems with the multi-point boundary condition. We investigate the convergence of the proposed method for the nonlinear problems with the multi-point boundary conditions. The obtained numerical results confirm the theoretical results and show the efficiency and accuracy of the proposed method.

Suggested Citation

  • Azarnavid, Babak & Emamjomeh, Mahdi & Nabati, Mohammad, 2022. "A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003691
    DOI: 10.1016/j.chaos.2022.112159
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    References listed on IDEAS

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    1. C. P. Zhang & J. Niu & Y. Z. Lin, 2012. "Numerical Solutions for the Three-Point Boundary Value Problem of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, June.
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    3. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher‐Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. C. P. Zhang & J. Niu & Y. Z. Lin, 2012. "Numerical Solutions for the Three‐Point Boundary Value Problem of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
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    1. Erfanifar, Raziyeh & Hajarian, Masoud, 2026. "A study on the convergence and efficiency of a novel seventh-order iterative method to solve systems of nonlinear equations with electrical engineering applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 650-664.

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