# neumann analysis using fourier series

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 October 23, 2002, 07:55 neumann analysis using fourier series #1 student Guest   Posts: n/a 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

 October 24, 2002, 08:55 Re: neumann analysis using fourier series #2 Tom Guest   Posts: n/a 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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