| Abstract: |
| We propose a linear difference scheme for a non-local conservative Allen--Cahn equation based on a combination of the discrete variational derivative method (DVDM) and a linearization technique. DVDM is a numerical method for designing schemes for PDEs. DVDM schemes inherit conservative or dissipative properties from the original PDEs in a discrete sense. By this approach, we obtain a nonlinear scheme in general, in which the current state is decided by a nonlinear relation concerning the previous state. Then, we need some iterative solver such as the Newton method to solve the system. This means that the computational cost is expensive. Therefore, we also use a linearization technique. The basic idea of our linearization technique is the decompositions of nonlinear terms by introducing extra time steps of numerical schemes. We expect that the proposed linear scheme is faster than the nonlinear one.
In this talk, we show the existence and uniqueness of a solution for the proposed scheme and stability. We also show numerical experiments. |
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