China
Africa
Explore chapters and articles related to this topic
Numerical Modeling and Simulation
Published in Yogesh Jaluria, Design and Optimization of Thermal Systems, 2019
A method similar to the Newton-Raphson method is the secant method, which uses interpolation and extrapolation to approximate the root in each iteration, employing the last two iterative values in the approximation. No derivatives are to be determined, as was the case for Newton's method. The iterative scheme is given by the equation xi+1=xi−1fxi−xifxi−1fxi−fxi−1
Algorithms in Static, Dynamic, Linear, and Non-Linear Finite Element Analyses
Published in Jie Shen, Radhey Lal Kushwaha, Soil-Machine Interactions, 2017
The secant method is another iterative approach which, in general, converges more quickly than the method of successive bisection. It also requires two points, x1 and x2, before starting an iterative process. To definitely control an iterative process, the restriction on the function f(x) is that in the domain (x1, x2), f(x) is continuous and the signs of both f′(x) and f″(x) do not change, where f′(x) and f″(x) are the first and second derivative of f at x, respectively.
Numerical Solution of Nonlinear Equations of One Variable
Published in Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, Padmanabhan Seshaiyer, Classical and Modern Numerical Analysis, 2009
Azmy S. Ackleh, Edward James Allen, Ralph Baker Hearfott, Padmanabhan Seshaiyer
(Convergence of the secant method) LetGbe a subset of ℝ containing a zeroz of f(x). Assumef∈C2(G)and there exists anM≥0such thatM=maxx∈Gf″(x)2minx∈Gf′(x).
Analytical Investigations of Reinforced Concrete Beam–Column Joints Constructed Using High-Strength Materials
Published in Journal of Earthquake Engineering, 2020
The Newton–Raphson method was applied to solve the nonlinear equations. In the regular Newton–Raphson method, the stiffness relation is evaluated in each iteration step. This method converges to the final answer within a few iterations as a quadratic convergence characteristic is shown by this method. Generally, the Newton–Raphson method needs a few iterations to converge, but each iteration step needs time to be done. On the other hand, the Quasi-Newton method (Secant method) uses the information of previous solution vectors and out-of-balance force vectors in order to come up with a better approximation of the solution. Iteration steps in this method are performed much faster compared to the regular Newton–Raphson method, which is desirable for the parametric investigation in this study. Hence, the Quasi-Newton iteration method is used to make a balance between the solution accuracy and the required computational effort.
A DA-based ECMS for energy optimisation of parallel diesel electric hybrid ship
Published in Ships and Offshore Structures, 2022
The secant method is a more effective method to solve such problems. Its advantage is that it does not use derivatives and has a super linear convergence rate. However, there are unavoidable limitations in the specific calculation, and the selection of its initial value has certain restrictions. In this paper, based on the secant method, in view of its shortcomings and limitations, an improved secant method is proposed. The improved secant method is used to quickly obtain the optimal value of equivalent factor in this paper.
Application of BWRS equation of state for calculation of fluid density and viscosity
Published in Petroleum Science and Technology, 2022
Yahui Li, Yihan Feng, Wei Wang, Jibin Zhong, Dandan Zhang
However, there is a problem in the calculation process of the secant method in that different convergence (ε) values have a considerable influence on the results of the calculation. When the density calculation of the pure-component propane is taken as an example, the pressure is 15 MPa and the temperatures are 293–393 K. The density results calculated using the secant method are shown in Figure 1.