Fortran Numerical Analysis Programs. The FORTRAN programs for some Numerical Method in. Write a Fortran program to find first derivation of the function f. An Introduction to Computational Physics Author: Tao Pang. All the Fortran 90 programs listed here are. Root Search with the secant method. On the other hand secant method starts with two. After each iteration the program should check to see if the convergence condition. Secant method solution. Numerical Mathematics and Computing. In the following table, each line/entry contains the program file name and a brief description. Sample Newton method: secant.f90: Secant method. Numerical Methods: FORTRAN Programs. Fortran Numerical Analysis Programs. = 3 x + sin x − e x using Secant method in the interval. Write a Fortran program to find first derivation of the.: Orthogonal polynomials generator. The most basic problem in Numerical Analysis (methods) is the root-finding problem. For a given function f (x), the process of finding the root involves. In the following table, each line/entry contains the program file name and a brief description. Click on the program name to display the source code, which can be downloaded. Chapter 1: Mathematical Preliminaries and Floating-Point Representation.
Although the Newton-Raphson method is very powerfull to solve non-linear equations, evaluating of the function derivative is the major difficulty of this method. To overcome this deficiency, the secant method starts the iteration by employing two starting points and approximates the function derivative by evaluating of the slope of the line passing through these points. The secant method has been shown in Fig. 1. As it is illustrated in Fig. 1, the new guess of the root of the function f(x) can be found as follows:
Fig. 1.The secant method
In the first glance, the secant method may be seemed similar to linear interpolation method, but there is a major difference between these two methods. In the secant method, it is not necessary that two starting points to be in opposite sign. Therefore, the secant method is not a kind of bracketing method but an open method. This major difference causes the secant method to be possibly divergent in some cases, but when this method is convergent, the convergent speed of this method is better than linear interpolation method in most of the problems.
The algorithm of the secant method can be written as follows:
Step 1: Choose two starting points x0 and x1.
Step 2: Let
Step 3: if |x2-x1|<ethen let root = x2, else x0 = x1 ; x1 = x2 ; go to step 2.
Step 4: End.
e: Acceptable approximated error.
oBisection Method
oLinear Interpolation Method
oModified Methods
oNewton-Raphson Method
Fortran Program For Secant Method Numerical Notation
oOne point Interpolation Method