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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED schemeS FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of Computational Mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(adi)scheme and the other is adi-PCG *** particular,we prove that adi scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis adi scheme PCG method

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A compact scheme for two-dimensional nonlinear time fractional wave equations

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第5期12卷 143-161页

作者： Guanghui Zhang Min Ren College of Mathematics and Statistics Suzhou University SuzhouAnhui 234000P.R.China

Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this end, an alternating direction implicit(adi) numerical scheme is derived. The scheme is established by combining the secondorder convolution quadrature formula and Crank–Nicolson technique in time and afourth-order difference approach in space. The convergence and unconditional stability of the proposed compact adi scheme are strictly discussed after a concise solvabilityanalysis. A numerical example is shown to demonstrate the theoretical analysis.

关键词： Two-dimensional nonlinear time fractional wave equations adi scheme convergence

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