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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 6.8

+//Scilab Version - 6.0.0 ; OS - Windows

+

+clc;

+clear;

+

+y=[15;50];                       //Constant coefficients in the equations

+x=[4;9];                         //Initial values for x1 and x2

+

+err=1;                           //Initialization of error value

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

+iter=0;                          //Initialization of iteration value

+

+while err>tol

+    temp=x;

+    f=[x(1)+x(2);x(1)*x(2)]                     //Function Value

+    dely=y-f;

+    J=[1 1;x(2) x(1)];                          //Jacobian Matrix

+    //Reduction of Jacobian using Gauss elimination

+    Jg=[J(1,1) J(1,2);0 J(2,2)-J(2,1)/J(1,1)]   

+    delyg=[dely(1);dely(2)-dely(1)*J(2,1)/J(1,1)]  

+    //Solution using back substitution

+    delx2=delyg(2)/Jg(2,2);

+    delx1=(delyg(1)-Jg(1,2)*delx2)/Jg(1,1)

+    delx=[delx1;delx2]

+    x=x+delx

+    err=max(abs((x(1)-temp(1))/temp(1)),abs((x(2)-temp(2))/temp(2)));

+    iter=iter+1;  

+    //Displaying first iteration results  

+    if iter==1

+        printf('Values of x1 and x2 at the end of first iteration are:\n')

+        printf('       x1=%.4f and x2=%.4f\n\n',x(1),x(2))

+    end

+end

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

+printf('The solution is x1=%.4f and x2=%.4f',x(1),x(2))

+