# Problems with equations discretization? (

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 October 21, 2003, 02:34 Problems with equations discretization? ( #1 Pr Guest   Posts: n/a 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)

 October 22, 2003, 03:09 Re: Problems with equations discretization? ( #2 Pr Guest   Posts: n/a Hi Peter on your request on other day. I have posted the complete problem to you. Any comments or suggestion on it. Pr

 October 22, 2003, 20:31 Re: Problems with equations discretization? ( #3 Peter Guest   Posts: n/a "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 ?

 October 23, 2003, 03:23 Re: Problems with equations discretization? ( #4 Pr Guest   Posts: n/a 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.

 October 30, 2003, 09:29 Re: Problems with equations discretization? ( #5 Pr Guest   Posts: n/a Hi, Peter,Pravin. Help me I am looking for your advice on the above problem Pr

 November 3, 2003, 19:55 Re: Problems with equations discretization? ( #6 Peter Guest   Posts: n/a "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.

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