We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponent...We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.展开更多
In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,...In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.19902002
文摘We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.
基金supported by National Natural Science Foundation of China(Grant No.12371409)supported by National Natural Science Foundation of China(Grant No.12271240)+1 种基金National Natural Science Foundation of China/Hong Kong Research Grants Council Joint Research Scheme(Grant No.11961160718)the Shenzhen Natural Science Fund(Grant No.RCJC20210609103819018)。
文摘In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.
