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Block-Centered Finite Difference Methods for Fourth-Order Parabolic Equations
Version 1
: Received: 17 May 2023 / Approved: 18 May 2023 / Online: 18 May 2023 (09:27:39 CEST)
A peer-reviewed article of this Preprint also exists.
Zhang, T.; Yin, Z.; Zhu, A. Block-Centered Finite-Difference Methods for Time-Fractional Fourth-Order Parabolic Equations. Fractal Fract. 2023, 7, 471. Zhang, T.; Yin, Z.; Zhu, A. Block-Centered Finite-Difference Methods for Time-Fractional Fourth-Order Parabolic Equations. Fractal Fract. 2023, 7, 471.
Abstract
In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.
Keywords
fourth-order parabolic equation; block-centered finite difference methods; stability; error estimates; numerical analysis
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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