Unformatted text preview: (d) Can one obtain a larger interval of absolute stability by relaxing the restriction on accuracy (e.g., accepting ﬁrst order accuracy)? Justify your answer. 3. Consider the equation u tt = u xx to be solved for ≤ x ≤ 1 , t > with initial data u ( x, 0) = u ( x ) u t ( x, 0) = u 1 ( x ) where u ,u 1 are smooth and vanishing near x = 0, x = 1. (a) Give boundary conditions at x = 0 and x = 1 to make this a well-posed problem. (b) Give a stable, convergent numerical approximation to this initial boundary value problem. 1...
View Full Document
- Spring '11
- Numerical Analysis, Boundary value problem, boundary value, utt, Dirichlet boundary conditions