Coupled system of linear elliptic PDE

[FrankST]

Hi,

I have a system of coupled PDE's as follows:

A1 * (f,xx + f,yy) + B1 * (g,xx + g,yy) + C1 * f + D1 * g = 0 ;

A2 * (f,xx + f,yy) + B2 * (g,xx + g,yy) + C2 * f + D2 * g = 0 ;

where, f = f(x,y) and g = g(x,y) and ,xx = second partial derivative of the function wrt x

and ,yy = second partial derivative of the function wrt y

A1, B1,..., D2 are constant coefficients.


It would be appreciated if you tell me how I can solve it analytically or numerically.


Thanks,

Frank

 

[gtoguy97]

The best way to solve such a system of equations is to use numerical methods. A popular approach is the finite element method, which involves discretizing the region of the problem into smaller elements and then solving the resulting linear system of equations. This approach will provide an approximate solution for the system of PDEs. Alternatively, you can try to make a transformation of the equations to turn it into an ordinary differential equation and then solve it analytically.