Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation
Xiaowei Chen, Xu Qian Xu Qian, Songhe Song
Abstract
We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order finite-difference semidiscretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is verified by several numerical examples.
Topics & Concepts
Lagrange multiplierRunge–Kutta methodsMathematicsMaximum principleAllen–Cahn equationSpace (punctuation)Applied mathematicsOrder (exchange)SpacetimeMathematical analysisFirst orderNumerical analysisMathematical optimizationComputer sciencePhysicsOptimal controlFinanceOperating systemEconomicsQuantum mechanicsSolidification and crystal growth phenomenaDifferential Equations and Numerical MethodsFluid Dynamics and Thin Films