Secant method to find root of a nonlinear equation using Matlab Solver

 

The Secant method is a numerical root-finding algorithm for finding the roots of a nonlinear equation. It is a modification of the Newton-Raphson method and is used when the derivative of the function is not readily available or difficult to compute.

The Secant method approximates the derivative of the function using a finite difference approximation and uses the approximation to iteratively update the initial guesses until a root is found. The method is based on the following formula:

xi+1 = xi - f(xi) * (xi - x(i-1)) / (f(xi) - f(x(i-1)))

where xi+1 is the updated guess for the root, xi and x(i-1) are the previous two guesses, and f(xi) and f(x(i-1)) are the values of the function at those two points.

The method starts with two initial guesses, x0 and x1, and computes the value of the function at those points. It then uses the formula above to compute a new guess, x2, and continues to update the guesses until the function value is close enough to zero.

The algorithm terminates when the absolute value of f(xi+1) is less than a specified tolerance, indicating that xi+1 is a close approximation to the root of the function.

The Secant method is generally slower than the Newton-Raphson method, but it is more robust and can be used in cases where the derivative is difficult to compute or not available. In short, it can be summarized as:

Secant method for finding the root of a non-linear equation can be solved using a hand or a math solver. Let us use a Matlab solver. Here is a sample code of secant method to solve equations of equations using Matlab.