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+//Book - Power System: Analysis & Design 5th Edition

+//Authors - J. Duncan Glover, Mulukutla S. Sarma, and Thomas J. Overbye

+//Chapter - 6 ; Example 6.6

+//Scilab Version - 6.0.0 ; OS - Windows

+

+clc;

+clear;

+

+//Solution for x^2=9 using Newton Raphson method:

+err=1;

+iternr=0;                   //Initial iteration value for Newton Raphson method

+tol=1e-4;                   //Tolerance value for Newton Raphson method

+xn=1;                       //Initial value for x for Newton Raphson method

+

+while err>tol

+     temp=xn;

+     J=2*xn;                  // Jacobian Matrix

+     xn=xn+inv(J)*(9-xn^2);

+     err=abs((xn-temp)/temp)

+     iternr=iternr+1;

+end

+

+//Solution for x^2=9 using Gauss–Seidel method

+err=1;

+D=3;

+itergs=0;                  //Initial iteration value for Gauss Seidal method

+xg=1;                      //Initial value for x for Gauss Seidal method

+

+while err>tol & itergs<iternr+1

+    temp=xg;

+    xg=xg+inv(D)*(9-xg^2)

+    err=abs((xg-temp)/temp)

+    itergs=itergs+1

+end

+printf('SOLUTION USING NEWTON RAPHSON METHOD:\n')

+printf('The convergence criterion is satisfied at the %dth iteration\n',iternr)

+printf('The solution is x=%.4f\n\n',xn)

+

+printf('SOLUTION USING GAUSS SEIDEL METHOD:\n')

+printf('The value for x at the end of %dth iteration\n',itergs)

+printf('is obtained as x=%.4f\n\n',xg)

+

+printf('COMPARISON:\n')

+if itergs>iternr

+    printf('Gauss Seidel method takes more time to converge')

+else

+    printf('Newton Raphson method takes more time to converge')

+end