Hi I have problem with discretizing the following equation.

u_t+(y**(1/3))[1+(u_y)^2]^{1/2}=c(t) where u_t and u_y is the partial differentials of u w.r.t t and y respectively. and c is the time varycoefficients let us say it is equal to sin(wt). I am using finite difference CN my solution blows up. y=[a:b] where b=2a.

Boundary condition to be used 1)when c(t)>=0 and u(a,t)=0,u_t=0. 2)when c(t)<0 or u(a,t)<0 u_x=0.

So Is there anybody who had already encountered such a problem. Please advice me.

Ps:I have discretixzed sucessfully the follwoing u_t+(y**(1/3))*[1+(u_y)^2]^{1/2}=c(t) when (y**(1/3))=A a constant. so that means u_t+A*[1+(u_y)^2]^{1/2}=c(t).

While the boundary condtions used was 1)when c(t)>=A and u(a,t)=0,u_t=0. 2)when c(t)<A or u(a,t)<0 u_x=0.

Hi Peter on your request on other day. I have posted the complete problem to you. Any comments or suggestion on it. Pr

"Boundary condition to be used 1)when c(t)>=0 and u(a,t)=0,u_t=0. 2)when c(t)<0 or u(a,t)<0 u_x=0."

why is the boundary condition changing with time ? The bc at x=a (which should be >0) should be independent of time. Is the blow-up coming at the time the bc switches from u=0 to u_x=0 ?

Thanks for the reply Peter.

Why should boundary condition be independent of time ?. See I already told you that I have solved the other equations and validated my results with prublished in paper with same boundary conditions. where A=constant then everything is okay even the boundary conditions.

Now changing A=x**1/3 why should I change my boundary condition why not keeping the same based upon the same analogy I have kept the same boundary condition.

Hi, Peter,Pravin. Help me I am looking for your advice on the above problem Pr

"I have solved the other equations and validated my results with

prublished in paper with same boundary conditions"

Can you give us the citation to that paper ? I am curious to see it. I am familiar with non-homogeneous dirichlet or neumann or robin type boundary conditions (where the forcing is a function of time) but I've never seen the _type_ of boundary condition to depend on time.