I want to solve it by MATLAB program
The non linear equations are:
log(x^2+y)-1+y=0;
sqrt(x)+xy=0,
initial approximation (x0,y0)=(2.4,-0.6)
no. of iteration is 50
The equation sqrt[x]=0 implies x=0. Consequently, the equation log[x^2+y]=0 reduces to log[y]=0, implying y=1. This result violates the equality 1+y = 0. Hence, the given set of equations has no solution.
I think the original post has been edited to correct the equations and the problem makes a bit more sense now. First let's call the two equations f1 and f2 resp. Then the Jacobian is
J = [ df1/dx df1/dy
df2/dx df2/dy ]
right? Straightforward analysis to get the partial derivatives. Below I use F = (f1,f2) and X = (x, y)
We can always evaluate the equations at our current point X(0) = (x0,y0)=(2.4,-0.6) that is we can get f1(x0,y0) and f2((x0,y0)..... and call that vector F(0). The NEXT point in our iterative scheme is found (lets call it m+1 from m), ....
X(m+1) = X(m) - J^-1 F(m)
where J is evaluated at our current iteration, and is "inverted."
Thank you all...... I got the solution and generated the code.
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