In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified var...This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method （MVIM） coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He＇s polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.展开更多
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
文摘This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method （MVIM） coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He＇s polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.
