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Convergence analysis of compact difference schemes for diffusion equation with nonlocal boundary conditions

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  • Cui, Ming Rong

Abstract

Compact difference schemes for solving the diffusion equation with nonlocal boundary conditions are considered in this paper. Fourth-order compact difference is used to approximate the second order spatial derivative, and the integrals in the boundary conditions are approximated by the composite Simpson quadrature formula. The backward Euler and Crank–Nicolson schemes are presented as the fully discrete schemes. Error estimates in the discrete h1 and l∞ norms are given by the energy method, showing both schemes are fourth-order accurate in space, and they have first-order and second-order accuracy in time, respectively. Numerical results are provided to confirm the theoretical results.

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  • Cui, Ming Rong, 2015. "Convergence analysis of compact difference schemes for diffusion equation with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 227-241.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:227-241
    DOI: 10.1016/j.amc.2015.03.039
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    1. Dehghan, Mehdi, 2007. "The one-dimensional heat equation subject to a boundary integral specification," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 661-675.
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    Cited by:

    1. Sapagovas, M. & Meškauskas, T. & Ivanauskas, F., 2018. "Influence of complex coefficients on the stability of difference scheme for parabolic equations with non-local conditions," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 228-240.

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