Alternating direction method for the wave equation with integral boundary conditions. (English) Zbl 1500.65046
Summary: We consider the stability of the alternating direction method for wave equation with integral boundary conditions in an energy norm. The proof of the stability is based on the properties of eigenvalues and eigenvectors of the corresponding difference operators. Numerical experiment is performed to confirm theoretical assumptions. Main properties of the alternating direction method are proven theoretically and numerically.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65H17 | Numerical solution of nonlinear eigenvalue and eigenvector problems |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L10 | Second-order hyperbolic equations |
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