,A SECOND-ORDER CONVEX SPLITTING SCHEME FOR A CAHN-HILLIARD EQUATION WITH VARIABLE INTERFACIAL PARAM

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In this paper,the MMC-TDGL equation,a stochastic Cahn-Hilliard equation with a variable interfacial parameter,is solved numerically by using a convex splitting scheme which is second-order in time for the non-stochastic part in combination with the Crank-Nicolson and the Adams-Bashforth methods.For the non-stochastic case,the unconditional energy stability is obtained in the sense that a modified energy is non-increasing.The scheme in the stochastic version is then obtained by adding the discretized stochastic term.Numerical experiments are carried out to verify the second-order convergence rate for the non-stochastic case,and to show the long-time stochastic evolutions using larger time steps.
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