I have the following PDE:$$u_{xx}u^3 - \sin(xt)u_{tt}=u(x,t)$$$$ u(x,0) = h,\u_t(x,0) = 1-h,\u_x(0,t)= h*u^3(0,t),\u_x(1,t)= 1$$where the problem is defined for $t>0$ and $x \in [0,1]$, and $h$ varies between $0$ and $1/2$.I want to simulate what happens to the solution $u(x,t)$ as $h$ changes between $0$ $1/2$ in steps of $0.01$.How do you suggest me to apply this in maple or matlab? I think that pdsolve in maple cannot handle this PDE; and I am not sure there's currently a good numerical method that will be of use to this problem of mine.
Simulation of parameter propagation of a numerical PDE solution
pde;numerical modelling