A symmetric fractional-order reduction method for direct nonuniform approximations of semilinear diffusion-wave equations

2021/01/24 by Pin Lyu, Lyu, Pin, Seakweng Vong +1 · 2 citations
Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2101.09678

Abstract

We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations. By using the novel order reduction method, the governing problem is transformed to an equivalent coupled system, where the explicit orders of time-fractional derivatives involved are all α/2 (1

Citations

• A second-order accurate numerical method for a fractional wave equation

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• Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm
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