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neumann analysis using fourier series

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Old   October 23, 2002, 07:55
Default neumann analysis using fourier series
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student
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Hai everyone I have partial differential equation of type del_U/del_t=t-(1+(del_u/del_x)^2)^0.5. now to get for neumann analysis using fourier series thanks in advance i want to use explicit finite difference scheme. How can I fix the delta t and delta x for this above example. thanks student

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Old   October 24, 2002, 08:55
Default Re: neumann analysis using fourier series
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Tom
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Why do you want to solve this equation using an explicit finite difference scheme? You can actually solve this equation analytically!

Assume u= F(x) at t=0 and let q(x) = F'(x) & p(x) = sqrt( 1 + q(x)^2 ).

Then for any specified x and t solve

n = x + ( q(n)/p(n) )t

for n with u then giving by u = F(n) + t( p(n)^2 - q(n)^2 )/p(n)

You can always do something like this for nonlinear first order pdes,

Tom.
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