In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and di...In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.展开更多
In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing resul...In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.展开更多
The theory of B-convergence for general linear methods is extended to general nonlinear muhivalue methods and to nonlinear stiff problems in Banach spaces. Moreover, using the extended theory, a class of high-order B-...The theory of B-convergence for general linear methods is extended to general nonlinear muhivalue methods and to nonlinear stiff problems in Banach spaces. Moreover, using the extended theory, a class of high-order B-convergent multistep-multiderivative methods is constructed.展开更多
Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusse...Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.展开更多
基金national natural science foundation natural science foundation of Gansu province.
文摘In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘The theory of B-convergence for general linear methods is extended to general nonlinear muhivalue methods and to nonlinear stiff problems in Banach spaces. Moreover, using the extended theory, a class of high-order B-convergent multistep-multiderivative methods is constructed.
文摘Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.
