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...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.展开更多
In this paper we develop a conservative local discontinuous Galerkin(LDG)method for the Schrödinger-Korteweg-de Vries(Sch-KdV)system,which arises in various physical contexts as a model for the interaction of lon...In this paper we develop a conservative local discontinuous Galerkin(LDG)method for the Schrödinger-Korteweg-de Vries(Sch-KdV)system,which arises in various physical contexts as a model for the interaction of long and short nonlinear waves.Conservative quantities in the discrete version of the number of plasmons,energy of the oscillations and the number of particles are proved for the LDG scheme of the Sch-KdV system.Semi-implicit time discretization is adopted to relax the time step constraint from the high order spatial derivatives.Numerical results for accuracy tests of stationary traveling soliton,and the collision of solitons are shown.Numerical experiments illustrate the accuracy and capability of the method.展开更多
基金the National Key R&D Program of China(No.2020YFA0709800)the National Key Project(No.GJXM92579)the National Natural Science Foundation of China(No.12071481)。
文摘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.
基金supported by the NSFC projects No.11101400Doctoral Fund of Ministry of Education of China No.20113402120015+1 种基金SRF for ROCS SEM.Research of Y.Xu is supported by NSFC grant No.10971211,No.11031007,FANEDD No.200916,NCET No.09-0922Fok Ying Tung Education Foundation No.131003.
文摘In this paper we develop a conservative local discontinuous Galerkin(LDG)method for the Schrödinger-Korteweg-de Vries(Sch-KdV)system,which arises in various physical contexts as a model for the interaction of long and short nonlinear waves.Conservative quantities in the discrete version of the number of plasmons,energy of the oscillations and the number of particles are proved for the LDG scheme of the Sch-KdV system.Semi-implicit time discretization is adopted to relax the time step constraint from the high order spatial derivatives.Numerical results for accuracy tests of stationary traveling soliton,and the collision of solitons are shown.Numerical experiments illustrate the accuracy and capability of the method.
