On the stability and convergence of discretizations of initial value p.d.e.s
This paper examines the stability and convergence of discretizations of initial value p.d.e.s using spatial discretization followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained re...
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| Format: | Journal article |
| Language: | English |
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1997
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| _version_ | 1797056136146321408 |
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| author | Giles, M |
| author_facet | Giles, M |
| author_sort | Giles, M |
| collection | OXFORD |
| description | This paper examines the stability and convergence of discretizations of initial value p.d.e.s using spatial discretization followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding sufficient conditions for both algebraic and strong stability. Sufficient conditions are also derived for convergence on a finite time interval. |
| first_indexed | 2024-03-06T19:19:07Z |
| format | Journal article |
| id | oxford-uuid:1970b5fe-b7e6-4f04-a8d6-e5a1ef182eeb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:19:07Z |
| publishDate | 1997 |
| record_format | dspace |
| spelling | oxford-uuid:1970b5fe-b7e6-4f04-a8d6-e5a1ef182eeb2022-03-26T10:49:05ZOn the stability and convergence of discretizations of initial value p.d.e.sJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1970b5fe-b7e6-4f04-a8d6-e5a1ef182eebEnglishSymplectic Elements at Oxford1997Giles, MThis paper examines the stability and convergence of discretizations of initial value p.d.e.s using spatial discretization followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding sufficient conditions for both algebraic and strong stability. Sufficient conditions are also derived for convergence on a finite time interval. |
| spellingShingle | Giles, M On the stability and convergence of discretizations of initial value p.d.e.s |
| title | On the stability and convergence of discretizations of initial value p.d.e.s |
| title_full | On the stability and convergence of discretizations of initial value p.d.e.s |
| title_fullStr | On the stability and convergence of discretizations of initial value p.d.e.s |
| title_full_unstemmed | On the stability and convergence of discretizations of initial value p.d.e.s |
| title_short | On the stability and convergence of discretizations of initial value p.d.e.s |
| title_sort | on the stability and convergence of discretizations of initial value p d e s |
| work_keys_str_mv | AT gilesm onthestabilityandconvergenceofdiscretizationsofinitialvaluepdes |