The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and...The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.展开更多
This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Ber...This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.展开更多
We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a ...We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.展开更多
The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatib...The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatibility can be examined in terms of the distribution of station residuals.For an ideal distribution,the input error is held at the station where it takes place as the station residual and the error is not permitted to spread to other stations.A comparison study of two optimization methods,namely the least squares method and the absolute value method,shows that the distribution with this character constrains the input errors and minimizes their impact,which explains the much more robust performance by the absolute value method in dealing with large and isolated input errors.When the errors in the input data are systematic and/or extreme in that the basic data structure is altered by these errors,none of the optimization methods are able to function.The only means to resolve this problem is the early detection and correction of these errors through a data screening process.An efficient data screening process is of primary importance for AE/MS source location.In addition to its critical role in dealing with those systematic and extreme errors,data screening creates a favorable environment for applying optimization methods.展开更多
Fourth order differential equations are considered to develop the class of methods for the numerical solution of boundary value problems. In this paper, we have discussed the regions of absolute stability of fourth or...Fourth order differential equations are considered to develop the class of methods for the numerical solution of boundary value problems. In this paper, we have discussed the regions of absolute stability of fourth order boundary value problems. Methods proposed and derived in this paper are applied to solve a fourth-order boundary value problem. Numerical results are given to illustrate the efficiency of our methods and compared with exact solution.展开更多
In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenilla...In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.展开更多
文摘The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.
文摘This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.
文摘We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.
文摘The efficiency of an optimization method for acoustic emission/microseismic（AE/MS） source location is determined by the compatibility of its error definition with the errors contained in the input data.This compatibility can be examined in terms of the distribution of station residuals.For an ideal distribution,the input error is held at the station where it takes place as the station residual and the error is not permitted to spread to other stations.A comparison study of two optimization methods,namely the least squares method and the absolute value method,shows that the distribution with this character constrains the input errors and minimizes their impact,which explains the much more robust performance by the absolute value method in dealing with large and isolated input errors.When the errors in the input data are systematic and/or extreme in that the basic data structure is altered by these errors,none of the optimization methods are able to function.The only means to resolve this problem is the early detection and correction of these errors through a data screening process.An efficient data screening process is of primary importance for AE/MS source location.In addition to its critical role in dealing with those systematic and extreme errors,data screening creates a favorable environment for applying optimization methods.
文摘Fourth order differential equations are considered to develop the class of methods for the numerical solution of boundary value problems. In this paper, we have discussed the regions of absolute stability of fourth order boundary value problems. Methods proposed and derived in this paper are applied to solve a fourth-order boundary value problem. Numerical results are given to illustrate the efficiency of our methods and compared with exact solution.
文摘In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.
