MATLAB: Solving 54 linear equations

source panel method

Hello, I am trying to solve 54 linear equations for the source panel method in Aerodynamics. I am using a for loop. These equations contain a symbolic variable lambda (the solution should be 54 lambdas of different values.

I tried using solve and vpasolve but it is taking a lot of time to compute. What should I do?.

Best Answer

Hello, you can use the strong point of MATLAB that is operating with arrays.

I'm not sure I understand the probem you're facing but, it can be just one of the following two scenarios:

CASE 1) You're dealing with 54 equations, the unknown is just lambda for each of them.

You can rewrite your equations in form of arrays as it follows:

A*x = b ==> x = b./A, where "A" is a column vector constituted of constans, "x" is a column vector containing your lambda values and finally, "b" is the column vector of known terms.

CASE 2) You're dealing with a system of 54 equations.

It's quite the same but, in this case "A" is a 54 x 54 Matrix (see link below to understand how to compute it).

You can solve the system in taht way: x = b\A.

In both cases you don't need to use symbolic variables, this method is much faster.

You can find a reference at the following link: https://en.wikipedia.org/wiki/System_of_linear_equations

I hope it helps. Kind Regards,

PGP

Related Solutions

MATLAB: How to evaluate a unknown variable

Using fsolve:

alpha=0.9;
g=[3, 2, 1];
N=10;
P=5;
f = @(lambda) sum(( lambda*(2-alpha)-sqrt(lambda*alpha*(lambda*alpha+g.*4*(1-alpha))) ) ...
    ./ ( g.*2*lambda*(alpha-1) )) - N*P;
lambda0 = 1;
options = optimoptions('fsolve','Display','iter','Algorithm','levenberg-marquardt');
lambda = fsolve(f, lambda0, options);