I have 4 coupled equations as below and I want to find the evolution of the system in time for parameters Y(x,t), R(x,t), T(x,t)  and W(x,t) which are scalars, scalar, vector and tensor in order.the system is 2d( i and j could be 1 or 2.)equations are as below:equationsK, d, a, v and b are constants. Any solution is highly appreciated.could anyone help me? Boundary condition: normal derivatives of R,W,Y and T on the boundary of a square with length L is zero. At t=0, R=r, Y=y and W=T=0.(y and r are some constants)
Discretization and simulation of coupled equations (pde)
nonlinear equations;discretization;nonlinear programming;coupling