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Unformatted text preview: hybrid, RKW3-θ scheme to integrate this problem. 2. Estimate the maximum value of Δ t = Δ t max that can be used to integrate this problem. 3. Solve the problem for 0 ≤ t ≤ 1 using N = 16 , 64 , 128 , 2048 grid points in x and Δ t = 0 . 2Δ t max . 4. Compare the solutions obtained in the previous step at t = 0 . 25 , . 5 , . 75 , 1 in terms of u ( x ) and | b u n | . Explain their time evolutions and their diﬀerences. 5. Is there Gibbs error in the previous solutions? Why? 6. Include a 6 th-order hyperviscosity regularization term ±∂ 6 x u in the equation with ± = 10-3 ν and repeat steps 2-5. Discuss the eﬀect of the regularization term. 7. Remove the non-linear term u∂ x u and repeat steps 2-5. Discuss the eﬀect of removing this term in the solution....
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- Spring '10
- Fourier Series, Partial differential equation, pseudospectral Fourier method