A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general piecewise alternately advanced and retarded argument.
In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s equations.The suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,pertu...In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s equations.The suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or restrictive assumptions.Numerical results reveal the complete reliability of the proposed VPM.展开更多
It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes,such as nano-hydrodynamics,drop wise condensation,oceanography,earthquake and wind ripple in desert...It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes,such as nano-hydrodynamics,drop wise condensation,oceanography,earthquake and wind ripple in desert.Inspired and motivated by these facts,we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations.The proposed technique is applied without any discretization,perturbation,transformation,restrictive assumptions and is free from Adomian’s polynomials.Several examples are given to verify the reliability and efficiency of the proposed technique.展开更多
This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ord...This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.展开更多
Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illust...Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.展开更多
In this paper,we use the modified variation of parameters method(MVPM),an elegant coupling of variation of parameters method(VPM)and Adomian’s decomposition method(ADM),for finding the analytical solution of system o...In this paper,we use the modified variation of parameters method(MVPM),an elegant coupling of variation of parameters method(VPM)and Adomian’s decomposition method(ADM),for finding the analytical solution of system of nonlinear fractional boundary value problems associated with obstacle.Caputo sense of fractional derivative is used to coup up with fractional term.The results are calculated in terms of series with easily computable components.The used technique is quite easy and convenient for such type problems because it has been previously applied over several nonlinear obstacle systems.展开更多
Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot...Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot. In this paper, we propose two control strategies to eliminate the secular growth of the argument of the perigee for orbits that are not at the critical inclination. One control strategy is using transverse continuous low-thrust, and the other is using both the transverse and the radial continuous low-thrusts. Fuel optimization in the second control strategy is addressed to make sure that the fuel consumption is the minimum. Both strategies have no effect on other orbital parameters’ secular motion. It is proved that the strategy with transverse control could save more energy than the one with radial control. Simulations show that the second control strategy could save 54.6% and 86% of energy, respectively, compared with the two methods presented in the references.展开更多
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for...A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.展开更多
基金supported by FONDECYT 1080034APIS 29-11 DIUMCEDI 0052-10 UNAP
文摘A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general piecewise alternately advanced and retarded argument.
文摘In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s equations.The suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or restrictive assumptions.Numerical results reveal the complete reliability of the proposed VPM.
基金This research is supported by the Visiting Professor Program of King Saud University,Riyadh,Saudi Arabia and Research grant No.KSU.-VPP.108.
文摘It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes,such as nano-hydrodynamics,drop wise condensation,oceanography,earthquake and wind ripple in desert.Inspired and motivated by these facts,we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations.The proposed technique is applied without any discretization,perturbation,transformation,restrictive assumptions and is free from Adomian’s polynomials.Several examples are given to verify the reliability and efficiency of the proposed technique.
文摘This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.
基金supported by the National Natural Science Foundation of China (10702078)the Research Foundation of National University of Defense Technology (JC08-01-05)
文摘Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.
文摘In this paper,we use the modified variation of parameters method(MVPM),an elegant coupling of variation of parameters method(VPM)and Adomian’s decomposition method(ADM),for finding the analytical solution of system of nonlinear fractional boundary value problems associated with obstacle.Caputo sense of fractional derivative is used to coup up with fractional term.The results are calculated in terms of series with easily computable components.The used technique is quite easy and convenient for such type problems because it has been previously applied over several nonlinear obstacle systems.
基金supported by the National Natural Science Foundation of China (Grant No 10702078)the Research Foundation of National University of Defense Technology (Grant No JC08-01-05)
文摘Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot. In this paper, we propose two control strategies to eliminate the secular growth of the argument of the perigee for orbits that are not at the critical inclination. One control strategy is using transverse continuous low-thrust, and the other is using both the transverse and the radial continuous low-thrusts. Fuel optimization in the second control strategy is addressed to make sure that the fuel consumption is the minimum. Both strategies have no effect on other orbital parameters’ secular motion. It is proved that the strategy with transverse control could save more energy than the one with radial control. Simulations show that the second control strategy could save 54.6% and 86% of energy, respectively, compared with the two methods presented in the references.
文摘A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
