present a class of eztendcd one-step time integration schemes for the integration of second-order nonlinear hyperbolic equations utt = c% 25 + p(z, t, u), subject to initial conditions and boundary conditions of Dirichlet type or of Neumann type. We obtain one-step time integration schemes of orders
โฆ LIBER โฆ
On a class of weighted additive schemes for second-order hyperbolic equations of arbitrary dimension
โ Scribed by V. A. Asmolik
- Book ID
- 110661848
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 324 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0012-2661
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We shall use below the local nurabering of the nodes, assigning local numbers 1,2,3 respectively to the nodes with coordinates (z,-,, it), (zm+t, tk), (x~, t~+,) . On Taylor-expanding the functions u, F up to second order terms in the neighborhoods of the nodes, we can write approximately ~m+| \*m