In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra in...In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.展开更多
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k, l)- algebraic...This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k, l)- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of (k, /)-algebraically stable Runge-Kutta methods are obtained.展开更多
In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of ...In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of these examples indi-cated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.展开更多
基金This work is supported partially by SRF for ROCS, SEM, NSERC (Canada) and NSF grant DMS-9704621.
文摘In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
基金supported by National Natural Science Foundation of China (No. 11171125,91130003)Natural Science Foundation of Hubei (No. 2011CDB289)Youth Foundation of Naval University of Engineering (No.HGDQNJJ10003)
文摘This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k, l)- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of (k, /)-algebraically stable Runge-Kutta methods are obtained.
文摘In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of these examples indi-cated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.