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 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
Purpose: This study aimed to clarify the relationship between respiratory muscle strength and balance in older people requiring support or nursing care. Methods: Thirty-seven older subjects aged 65 years or older who ...Purpose: This study aimed to clarify the relationship between respiratory muscle strength and balance in older people requiring support or nursing care. Methods: Thirty-seven older subjects aged 65 years or older who were certified as requiring nursing care or support were included in the study. Maximal inspiratory pressure (PIMAX), maximal expiratory pressure (PEMAX), and one-leg standing time were measured. Additionally, the Functional Reach Test (FRT) was performed. Pearson correlation coefficient and multiple regression analyses were performed. Results: One-leg standing time was positively correlated with PEMAX, and was particularly correlated with PIMAX, while FRT score was not correlated with respiratory muscle strength. Multiple regression analysis with one-leg standing time as the dependent variable and PIMAX and PEMAX as independent variables showed that only PIMAX was significantly correlated with one-leg standing time. Conclusion: Focusing on expiratory and inspiratory muscle strength is important for improving one-leg standing ability and thus preventing falls in older people.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
The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructi...The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.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
Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle ...Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle activation patterns between 2-legged and 1-legged pedaling.Methods:Fifteen healthy young recreational cyclists performed both 1-legged and 2-legged pedaling trials at about 30 Watt per leg.Surface electromyography electrodes were placed on 10 major muscles of the left leg.Linear envelope electromyography data were integrated to quantify muscle activities for each crank cycle quadrant to evaluate muscle activation changes.Results:Overall,the prescribed constant power requirements led to reduced downstroke crank torque and extension-related muscle activities(vastus lateralis,vastus medialis,and soleus)in 1-legged pedaling.Flexion-related muscle activities(biceps femoris long head,semitendinosus,lateral gastrocnemius,medial gastrocnemius,tensor fasciae latae,and tibialis anterior)in the upstroke phase increased to compensate for the absence of contralateral leg crank torque.During the upstroke,simultaneous increases were seen in the hamstrings and uni-articular knee extensors,and in the ankle plantarflexors and dorsiflexors.At the top of the crank cycle,greater hip flexor activity stabilized the pelvis.Conclusion:The observed changes in muscle activities are due to a variety of changes in mechanical aspects of the pedaling motion when pedaling with only 1 leg,including altered crank torque patterns without the contralateral leg,reduced pelvis stability,and increased knee and ankle stiffness during the upstroke.展开更多
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
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.
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.
文摘Purpose: This study aimed to clarify the relationship between respiratory muscle strength and balance in older people requiring support or nursing care. Methods: Thirty-seven older subjects aged 65 years or older who were certified as requiring nursing care or support were included in the study. Maximal inspiratory pressure (PIMAX), maximal expiratory pressure (PEMAX), and one-leg standing time were measured. Additionally, the Functional Reach Test (FRT) was performed. Pearson correlation coefficient and multiple regression analyses were performed. Results: One-leg standing time was positively correlated with PEMAX, and was particularly correlated with PIMAX, while FRT score was not correlated with respiratory muscle strength. Multiple regression analysis with one-leg standing time as the dependent variable and PIMAX and PEMAX as independent variables showed that only PIMAX was significantly correlated with one-leg standing time. Conclusion: Focusing on expiratory and inspiratory muscle strength is important for improving one-leg standing ability and thus preventing falls in older people.
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.
文摘The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.
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.
基金supported by the University of Massachusetts Amherst(SP:Graduate School Fellowship,and School of Public Health and Health Sciences Dean’s PhD Summer FellowshipGEC:Faculty Research Grant).
文摘Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle activation patterns between 2-legged and 1-legged pedaling.Methods:Fifteen healthy young recreational cyclists performed both 1-legged and 2-legged pedaling trials at about 30 Watt per leg.Surface electromyography electrodes were placed on 10 major muscles of the left leg.Linear envelope electromyography data were integrated to quantify muscle activities for each crank cycle quadrant to evaluate muscle activation changes.Results:Overall,the prescribed constant power requirements led to reduced downstroke crank torque and extension-related muscle activities(vastus lateralis,vastus medialis,and soleus)in 1-legged pedaling.Flexion-related muscle activities(biceps femoris long head,semitendinosus,lateral gastrocnemius,medial gastrocnemius,tensor fasciae latae,and tibialis anterior)in the upstroke phase increased to compensate for the absence of contralateral leg crank torque.During the upstroke,simultaneous increases were seen in the hamstrings and uni-articular knee extensors,and in the ankle plantarflexors and dorsiflexors.At the top of the crank cycle,greater hip flexor activity stabilized the pelvis.Conclusion:The observed changes in muscle activities are due to a variety of changes in mechanical aspects of the pedaling motion when pedaling with only 1 leg,including altered crank torque patterns without the contralateral leg,reduced pelvis stability,and increased knee and ankle stiffness during the upstroke.
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
