A Fast Two-Level Strang Splitting Method for Multi-Dimensional Spatial Fractional Allen-Cahn Equations with Discrete Maximum Principle
نویسندگان
چکیده
منابع مشابه
A second order operator splitting method for Allen–Cahn type equations with nonlinear source terms
Allen–Cahn (AC) type equations with nonlinear source terms have been applied to a wide range of problems, for example, the vector-valued AC equation for phase separation and the phase-field equation for dendritic crystal growth. In contrast to the well developed first and second order methods for the AC equation, not many second order methods are suggested for the AC type equations with nonline...
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We consider numerical methods for solving the fractional-in-space Allen-Cahn (FiSAC) equation which contains small perturbation parameters and strong noninearilty. Standard fully discretized schemes for the the FiSAC equation will be considered, namely, in time the conventional first-order implicit-explicit scheme or second-order Crank-Nicolson scheme and in space a secondorder finite differenc...
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Article history: Received 10 May 2013 Received in revised form 18 July 2014 Accepted 2 August 2014 Available online 8 August 2014
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Abstract. Using the method of sub-super-solution, we construct a solution of (−∆)su − cuz − f(u) = 0 on R of pyramidal shape. Here (−∆)s is the fractional Laplacian of sub-critical order 1/2 < s < 1 and f is a bistable nonlinearity. Hence, the existence of a traveling wave solution for the parabolic fractional Allen-Cahn equation with pyramidal front is asserted. The maximum of planar traveling...
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It has recently been proposed that spatially discretized versions of the Allen-Cahn and Cahn-Hilliard equations for modeling phase transitions have certain theoretical and phenomenological advantages over their continuous counterparts. This paper deals with one-dimensional discretizations and examines the extent to which dynamical metastability, which manifests itself in the original partial di...
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ژورنال
عنوان ژورنال: East Asian Journal on Applied Mathematics
سال: 2023
ISSN: ['2079-7362', '2079-7370']
DOI: https://doi.org/10.4208/eajam.2022-248.161022