• Bisection Method In C
• Basic Fortran Programs

Bisection Method In C

Basic Fortran Programs

The program can run calculations in one of the following methods: modified Euler, Runge-Kutta 4th order, and Fehlberg fourth-fifth order Runge-Kutta method. To run the code following programs should be included: euler22m.f, rk4d22.f, rkf45.f. An example using the bisection method to solve for the root of an equation. Tutorials by MATLAB Marina.

ExamplesExample 1Consider finding the root of f( x) = x 2 - 3. Letε step = 0.01, ε abs = 0.01 and start with the interval 1, 2.Table 1. Bisection method applied to f( x) = x 2 - 3. Abf( a)f( b)c = (a + b)/2f( c)Updatenew b − a1.02.0-2.01.01.5-0.75a = c0.51.52.0-0.751.01.750.062b = c0.251.51.75-0.750.06251.625-0.359a = c0.1251.6251.75-0.1.6875-0.1523a = c0.1.75-0.1.7188-0.0457a = c0.1.75-0.1.b = c0.8/td 1.7344-0.1.7266-0.0189a = c0.0078Thus, with the seventh iteration, we note that the final interval, 1.7266, 1.7344,has a width less than 0.01 and f(1.7344).