Focuses on a study which explored the numerical solution of delay differential equations. Linear stability of numerical methods; Application of one-leg methods; Error analysis.
This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear in...This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear interpolation procedure is D-convergent of oder p if and only if it is A-stable and consistent of order p in the classical sense for ODEs. The results obtained can be regarded as extension of that for DDEs with constant delay presented by Huang Chenming et al. in展开更多
This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We obtain convergence results of A-stable one-leg ...This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We obtain convergence results of A-stable one-leg methods with linear interpolation procedure. Numerical experiments further confirm our theoretical analysis.展开更多
Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs...Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper.展开更多
This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable ... This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable one-leg methods with linear interpolation procedure.展开更多
Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confi...Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.展开更多
文摘Focuses on a study which explored the numerical solution of delay differential equations. Linear stability of numerical methods; Application of one-leg methods; Error analysis.
文摘This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear interpolation procedure is D-convergent of oder p if and only if it is A-stable and consistent of order p in the classical sense for ODEs. The results obtained can be regarded as extension of that for DDEs with constant delay presented by Huang Chenming et al. in
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 19871086 & 10101027 ).
文摘This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We obtain convergence results of A-stable one-leg methods with linear interpolation procedure. Numerical experiments further confirm our theoretical analysis.
基金supported by National Natural Science Foundation of China (Grant No. 10871164)the Natural Science Foundation of Hunan Province (Grant No. 08JJ6002)the Scientific Research Fund of Changsha University of Science and Technology (Grant No. 1004259)
文摘Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper.
基金the National Natural Science Fundation of China (No.19871086&10101027)China Postdoctoral Science Foundationa.
文摘 This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable one-leg methods with linear interpolation procedure.
基金This work is supported by NSF of China(10971175)Specialized Research Fund for the Doctoral Program of Higher Education of China(20094301110001)+2 种基金Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)NSF of Hunan Province(10JJ7001)the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province,and Fund Project of Hunan Province Education Office(11C1220).
文摘Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.
