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Old   October 21, 2003, 02:34
Default Problems with equations discretization? (
  #1
Pr
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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.
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Old   October 22, 2003, 03:09
Default Re: Problems with equations discretization? (
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Pr
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Hi Peter on your request on other day. I have posted the complete problem to you. Any comments or suggestion on it. Pr
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Old   October 22, 2003, 20:31
Default Re: Problems with equations discretization? (
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Peter
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"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 ?
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Old   October 23, 2003, 03:23
Default Re: Problems with equations discretization? (
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Pr
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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.

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Old   October 30, 2003, 09:29
Default Re: Problems with equations discretization? (
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Pr
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Hi, Peter,Pravin. Help me I am looking for your advice on the above problem Pr
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Old   November 3, 2003, 19:55
Default Re: Problems with equations discretization? (
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Peter
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"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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