A MATLAB Program to Determine the Roots of Equation by Secant method

Problem: Solve the following problem by Secant Method.

f(x) = x - 2e^-x

Determine the roots of the above function where x1 = 0 and x2 = 1.

Solution: The following MATLAB program solves this problem.

% Definition of a function "secantmethod" to solve equation by Secant Method

function [x,ea] = secantmethod(X,X0,etol)

format long;

% Input: X=0, etol=Tolerance definition for error

% Output x=Solution of equation, ea=Calculated error in loop

% Program Initialization

% Iterative Calculations

while (1)

   

    % Implementation of Secant Method

         

    solution = X-((X-(2*exp(-X)))*(X0-X))/((X0-(2*exp(-X0)))-(X-(2*exp(-X))));    

   

    solutionprevious=X;

    X0=X;

    X=solution;

                 

if (solution-solutionprevious)~=0          % Approximate percent relative error

                                

   ea=abs((solution - solutionprevious)/solution)*100;

      

end

if ea<=etol                 

  

    break,               

end

%x0=solutionprevious;

x = solution;

%disp(x0);

disp(x);

end

% Display of output parameters

disp(x);                     

disp(ea);

%disp(solution-(0.1*abs(ea)*solution));

end

Program Outputs:

>> secantmethod(1,0,1e-10)

   0.883298154248460

   0.851584208519236

   0.852612692886131

   0.852605503703827

   0.852605502013723

   0.852605502013723

     3.125167797776517e-13

ans =

   0.852605502013723

#SecantMethod