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An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation

Author

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  • Somayeh Pourghanbar
  • Jalil Manafian
  • Mojtaba Ranjbar
  • Aynura Aliyeva
  • Yusif S. Gasimov

Abstract

In this paper, the Saul’yev finite difference scheme for a fully nonlinear partial differential equation with initial and boundary conditions is analyzed. The main advantage of this scheme is that it is unconditionally stable and explicit. Consistency and monotonicity of the scheme are discussed. Several finite difference schemes are used to compare the Saul’yev scheme with them. Numerical illustrations are given to demonstrate the efficiency and robustness of the scheme. In each case, it is found that the elapsed time for the Saul’yev scheme is shortest, and the solution by the Saul’yev scheme is nearest to the Crank–Nicolson method.

Suggested Citation

  • Somayeh Pourghanbar & Jalil Manafian & Mojtaba Ranjbar & Aynura Aliyeva & Yusif S. Gasimov, 2020. "An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, November.
    • Handle: RePEc:hin:jnlmpe:9647416
    DOI: 10.1155/2020/9647416
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    Cited by:

    1. Miglena N. Koleva & Lubin G. Vulkov, 2024. "Numerical Reconstruction of Time-Dependent Boundary Conditions to 2D Heat Equation on Disjoint Rectangles at Integral Observations," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    2. Issa Omle & Ali Habeeb Askar & Endre Kovács & Betti Bolló, 2023. "Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges," Energies, MDPI, vol. 16(12), pages 1-27, June.
    3. Mahmoud Saleh & Endre Kovács & Imre Ferenc Barna & László Mátyás, 2022. "New Analytical Results and Comparison of 14 Numerical Schemes for the Diffusion Equation with Space-Dependent Diffusion Coefficient," Mathematics, MDPI, vol. 10(15), pages 1-26, August.

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