Spatial discretization of partial differential equations with integrals
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arXiv
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| Format: | Preprint |
| Publié: |
1998
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| _version_ | 1866908600133222400 |
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| author | McLachlan, Robert I |
| author_facet | McLachlan, Robert I |
| contents | We consider the problem of constructing spatial finite difference approximations on a fixed, arbitrary grid, which have analogues of any number of integrals of the partial differential equation and of some of its symmetries. A basis for the space of of such difference operators is constructed; most cases of interest involve a single such basis element. (The ``Arakawa'' Jacobian is such an element.) We show how the topology of the grid affects the complexity of the operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9808109 |
| institution | arXiv |
| publishDate | 1998 |
| record_format | arxiv |
| spellingShingle | Spatial discretization of partial differential equations with integrals McLachlan, Robert I Numerical Analysis Dynamical Systems We consider the problem of constructing spatial finite difference approximations on a fixed, arbitrary grid, which have analogues of any number of integrals of the partial differential equation and of some of its symmetries. A basis for the space of of such difference operators is constructed; most cases of interest involve a single such basis element. (The ``Arakawa'' Jacobian is such an element.) We show how the topology of the grid affects the complexity of the operators. |
| title | Spatial discretization of partial differential equations with integrals |
| topic | Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/math/9808109 |