To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce th...This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.展开更多
Aiming to improve the maneuver performance of the strapdown inertial navigation attitude coning algorithm a new coning correction structure is constructed by adding a sample to the traditional compressed coning correc...Aiming to improve the maneuver performance of the strapdown inertial navigation attitude coning algorithm a new coning correction structure is constructed by adding a sample to the traditional compressed coning correction structure. According to the given definition of classical coning motion the residual coning correction error based on the new coning correction structure is derived. On the basis of the new structure the frequency Taylor series method is used for designing a coning correction structure coefficient and then a new coning algorithm is obtained.Two types of error models are defined for the coning algorithm performance evaluation under coning environments and maneuver environments respectively.Simulation results indicate that the maneuver accuracy of the new 4-sample coning algorithm is almost double that of the traditional compressed 4-sample coning algorithm. The new coning algorithm has an improved maneuver performance while maintaining coning performance compared to the traditional compressed coning algorithm.展开更多
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.
基金The National Natural Science Foundation of China(No.51375087)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20110092110039)+2 种基金the Public Science and Technology Research Funds Projects of Ocean(No.201205035)the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXZZ12_0097)the Scientific Research Foundation of Graduate School of Southeast University(No.YBJJ1349)
文摘Aiming to improve the maneuver performance of the strapdown inertial navigation attitude coning algorithm a new coning correction structure is constructed by adding a sample to the traditional compressed coning correction structure. According to the given definition of classical coning motion the residual coning correction error based on the new coning correction structure is derived. On the basis of the new structure the frequency Taylor series method is used for designing a coning correction structure coefficient and then a new coning algorithm is obtained.Two types of error models are defined for the coning algorithm performance evaluation under coning environments and maneuver environments respectively.Simulation results indicate that the maneuver accuracy of the new 4-sample coning algorithm is almost double that of the traditional compressed 4-sample coning algorithm. The new coning algorithm has an improved maneuver performance while maintaining coning performance compared to the traditional compressed coning algorithm.
