High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation. (English) Zbl 07763842
Summary: We utilize the second-order quadrature-based finite difference method and the high-order parametric integrating factor Runge-Kutta (pIFRK) integrators to construct efficient and accurate schemes for solving the nonlocal Allen-Cahn equation. These schemes preserve the maximum principle for any time-step, and exhibit up to fourth-order accuracy in the temporal direction. We establish a rigorous error estimate and an asymptotic compatibility analysis for the pIFRK schemes. Numerical experiments demonstrate the accuracy and structure-preserving property of the proposed schemes, verify their asymptotic compatibility, and investigate the discontinuity of the nonlocal Allen-Cahn equation under certain conditions.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 65Lxx | Numerical methods for ordinary differential equations |
| 35Kxx | Parabolic equations and parabolic systems |
Keywords:
parametric integrating factor Runge-Kutta method; nonlocal Allen-Cahn equation; maximum-principle-preservationReferences:
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