CODEWITHSUNDEEP
matlabmathgraphplotequation
Vijay13
Vijay13

Reputation: 605

How do I plot non linear equation in MATLAB?

Equation: 

0 = x*114 - x*log3(x) - 20.28*y

I have Y = 10^3, 10^6, 10^9, 10^12, 10^15, ..... and above mentioned equation. How do I solve (i.e. getting values of x for different y) and plot this equation in MATLAB ?

Upvotes: 0

Views: 102

Answers (1)

AnonSubmitter85
AnonSubmitter85

Reputation: 933

Assuming that the solution is unique, one way to solve the equation is numerically:

y = 10.^(3:3:15);
opts = optimset( 'TolFun', 1e-9, 'TolX', 1e-9, 'MaxIter', 1e6, 'MaxFunEvals', 1e6 );
for ii = 1 : length(y);
  fcost = @(x)( x*114 - x*log10(x)/log10(3) - 20.28*y(ii) ).^2;
  xopt(ii) = fminsearch( fcost, y(ii), opts );
  fprintf( 1, 'y = %-5g : x = %-17.15g : f(xopt) = %-17.15g\n', ...
    y(ii), xopt(ii), fcost(xopt(ii)) );
end

% Plot the answers on a log-log scale.
loglog( xopt, y, 'k*' );

The above produces the following output, so we can see that the solutions are valid.

y = 1000  : x = 185.637624348601  : f(xopt) = 6.37079420013969e-17
y = 1e+06 : x = 197078.905034998  : f(xopt) = 8.88178419700125e-16
y = 1e+09 : x = 210030727.535742  : f(xopt) = 5.82076609134674e-11
y = 1e+12 : x = 224814576366.276  : f(xopt) = 1.52587890625e-05
y = 1e+15 : x = 241850436303022   : f(xopt) = 0

There might be a better symbolic way to do it, but the above will work. I just guessed at the starting point for the search by setting it equal to y. If you need more accuracy in the solution, look at help optimset and help fminsearch. There are arguments that you can pass in that control the accuracy of the solution and when the search will terminate.

Upvotes: 1

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