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Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions

Author

Listed:
  • Makhmud A. Sadybekov

    (Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
    Depatment of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan)

  • Irina N. Pankratova

    (Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan)

Abstract

For a nonlocal initial-boundary value problem for a one-dimensional heat equation with not strongly regular boundary conditions of general type, an approximate difference scheme with weights is constructed. A correct and stable algorithm for the numerical solving of the difference problem is proposed. It is proven that the difference scheme with weights is stable and its solution converges to the exact solution of the differential problem in the grid L 2 h -norm. Stability conditions are established. An estimate of the numerical solution with respect to the initial data and the right-hand side of the difference problem is given.

Suggested Citation

  • Makhmud A. Sadybekov & Irina N. Pankratova, 2022. "Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3780-:d:941472
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    References listed on IDEAS

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    1. Želi, Velibor & Zorica, Dušan, 2018. "Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2316-2335.
    2. Alexander S. Makin, 2012. "On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-13, September.
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