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Unformatted text preview: dt = .001; % Defining an appropriate time step. u0 = zeros(1,N); %Defining the initial data u0(N/2+1:N)= ones(1,N/2); % Defining the initial data k=(1i*[0:N/21 0 N/2+1:1]); k3=k.^3; u=ifft(exp(k3*t).*fft(u0));%Solution to the Linearly dispersive wave equation. plot(u)%Command to plot the solution At time t = . 05 * Ï€ , using the above code we get the following ï¬gure: 1 Using the exact solution, we get: At an irrational multiple of Ï€ , we notice a fractal pattern to the graph: and the exact solution produces the same plot 2...
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 Spring '08
 wormer
 Partial differential equation, Fundamental physics concepts, convolution theorem, Sudarshan Balakrishnan

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