youthnax.blogg.se - Fortran program for secant method examples

The following illustrations indicate some of the difficulties that can occur when one has a poor guess and some pathological behavior of the equation.

Iterate Graphically this can be depicted as: One of the problems with the Newton method is that one needs a good first guess, especially for multidimensional problems.

Calculate f(x) and the derivative f’(x), i.e., df(x)/dx.

Newton’s method (Newton-Raphson method) Newton’s method consists of four steps: Depending on how accurately you need to know the solution, this method should give you the answer you need relatively simply. Idiot’s method The simplest method that is relatively foolproof is to plot the function and see where it crosses the x axis. Thus the speed of computers makes the brute force approach an effective strategy. In short, one hour of computer time is worth about 1 human lifetime in mathematical problem solving.

A talented person might be able to do 1 operation/sec or about 4 x 10 8 operations in a lifetime. Why do we use this approach?Ī computer can do about 10 6 operations/sec or about 3.6 x 10 9 operations/hr. Some of the chemical examples include Weak acid/base equilibria titrations The vapor pressure equation, ln P = A + (B/T) + C ln T Equation of state problems Equilibrium calculations Quantum mechanics Kinetics The philosophy of finding roots of equations is to use a series of approximations and iteration to solve the problems, in short, to use brute force. There are many examples of chemical problems in which one needs to find the roots of equations.

One might ask what this has to do with chemistry or science, etc. Roots of Equations The root of a one dimensional equation is the value of x for which the equation y=f(x)=0. In such cases it may be necessary to rely on the first order and secant methods. The efficiency and convergence of this method.