Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
نویسندگان
چکیده
منابع مشابه
On the maximum principle preserving schemes for the generalized Allen-Cahn Equation
This paper is concerned with the generalized Allen-Cahn equation with a nonlinear mobility that can degenerate, which also includes an advection term as found in phase-field models. A class of maximum principle preserving schemes will be studied for the generalized Allen-Cahn equation, with either the commonly used polynomial free energy or the logarithmic free energy, and with a nonlinear dege...
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is the Allen-Cahn equation: ut = 4u(x)− f(u) (5) As mentioned in [3], the equations (1) and (5) are important for modelling a variety of physical and biological phenomena involving media with properties varying in space. There is by now a lot of work on equation (1) and (5) (see for example [1], [2], [5], [7], [8], [9], [11], [12], [13], [15], [16], [17], and the references therein). To the bes...
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It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-exp...
متن کاملOn the maximum principle and energy stability for fully discretized fractional-in-space Allen-Cahn equation
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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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2019
ISSN: 0036-1429,1095-7170
DOI: 10.1137/18m118236x