We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations...We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations of the periodic solutions to the (2+1)-dimensional KdV equations obtained by means of the Jacobian elliptic function method, but they possess different periods and velocities.展开更多
This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the ps...This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state(smooth state)and fast state(impulsive state)are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth(slow)response and the fast(implusive)response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given.展开更多
A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation ...A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the(2+1)-dimensional Kad...To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the(2+1)-dimensional Kadomtsev–Petviashvili(KP) equation, the(3+1)-dimensional generalized Kadomtsev–Petviashvili(g-KP) equation, and the B-type Kadomtsev–Petviashvili(BKP) equation. Aa a result, we obtain some new resonant multiple wave solutions through the parameterization for wave numbers and frequencies via some linear combinations of exponential traveling waves. Finally, these new resonant type solutions can be displayed in graphs to illustrate the resonant behaviors of multiple wave solutions.展开更多
For a SlSO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its correspond...For a SlSO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l1 norm objective.展开更多
A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds t...A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds this interface condition into its numerical flux is called the immersed interface upwind scheme. An ι1-error estimate of such a scheme was first established by Wen et al. （2008）. In this paper, we provide a simple analysis on the ι1-error estimate. The main idea is to formulate the solution to the underline initial-value problem into the sum of solutions to two convection equations with constant coefficients, which can then be estimated using classical methods for the initial or boundary value problems.展开更多
In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yi...In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.展开更多
基金国家自然科学基金，Research Foundation for Young Skeleton Teacher in College of Zhejiang Province，the Science Research Foundation of Huzhou University
文摘We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations of the periodic solutions to the (2+1)-dimensional KdV equations obtained by means of the Jacobian elliptic function method, but they possess different periods and velocities.
文摘This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state(smooth state)and fast state(impulsive state)are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth(slow)response and the fast(implusive)response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given.
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
基金Project supported by the Yue-Qi Scholar of the China University of Mining and Technology(Grant No.102504180004)the 333 Project of Jiangsu Province,China(Grant No.BRA2018320)
文摘To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the(2+1)-dimensional Kadomtsev–Petviashvili(KP) equation, the(3+1)-dimensional generalized Kadomtsev–Petviashvili(g-KP) equation, and the B-type Kadomtsev–Petviashvili(BKP) equation. Aa a result, we obtain some new resonant multiple wave solutions through the parameterization for wave numbers and frequencies via some linear combinations of exponential traveling waves. Finally, these new resonant type solutions can be displayed in graphs to illustrate the resonant behaviors of multiple wave solutions.
基金This work was supported by the National Science Foundation of China(No.60274036).
文摘For a SlSO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l1 norm objective.
基金supported by National Science Foundation of USA(Grant No.DMS1114546)
文摘A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds this interface condition into its numerical flux is called the immersed interface upwind scheme. An ι1-error estimate of such a scheme was first established by Wen et al. （2008）. In this paper, we provide a simple analysis on the ι1-error estimate. The main idea is to formulate the solution to the underline initial-value problem into the sum of solutions to two convection equations with constant coefficients, which can then be estimated using classical methods for the initial or boundary value problems.
文摘In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.
