The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution ...The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.展开更多
The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo se...The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.展开更多
In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem in...In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.展开更多
Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems.In this paper,a novel approach based on matrix perturbation theory is proposed for the calculation of eige...Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems.In this paper,a novel approach based on matrix perturbation theory is proposed for the calculation of eigen-solutions in a perturbed system.Rigorous theoretical analysis is conducted on the solution of distinct,multiple,and close eigen-solutions,respectively,under perturbations of parameters.The computational flowchart of the unified solution of eigen-solutions is then proposed,aimed toward obtaining eigen-solutions of a perturbed system directly with algebraic formulas without solving an eigenvalue problem repeatedly.Finally,the effectiveness of the matrix perturbation based approach for eigen-solutions’calculation in power systems is verified by numerical examples on a two-area four-machine system.展开更多
The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy-pe...The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy-perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian＇s decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian＇s decomposition method. Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions. The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations.展开更多
文摘The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.
文摘The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.
文摘In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.
基金supported in part by the National Science Foundation of United States(NSF)(Grant No.0844707)in part by the International S&T Cooperation Program of China(ISTCP)(Grant No.2013DFA60930)
文摘Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems.In this paper,a novel approach based on matrix perturbation theory is proposed for the calculation of eigen-solutions in a perturbed system.Rigorous theoretical analysis is conducted on the solution of distinct,multiple,and close eigen-solutions,respectively,under perturbations of parameters.The computational flowchart of the unified solution of eigen-solutions is then proposed,aimed toward obtaining eigen-solutions of a perturbed system directly with algebraic formulas without solving an eigenvalue problem repeatedly.Finally,the effectiveness of the matrix perturbation based approach for eigen-solutions’calculation in power systems is verified by numerical examples on a two-area four-machine system.
文摘The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy-perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian＇s decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian＇s decomposition method. Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions. The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations.
