Rapid convergence of approximate solutions for first order nonlinear boundary value problems
In this paper we study the convergence of the approximate solutions for the following first order problem u′(t)=f(t,u(t));t∈[0,T],au(0)−bu(t0)=c,a,b≥0,t0∈(0,T]. Here f:I×ℝ→ℝ is such that ∂kf∂uk exists and is a continuous function for some k≥1. Under some additional conditions on ∂f∂u, we prove that...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000714 |
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| _version_ | 1832566398395613184 |
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| author | Alberto Cabada Juan J. Nieto Seppo Heikkilä |
| author_facet | Alberto Cabada Juan J. Nieto Seppo Heikkilä |
| author_sort | Alberto Cabada |
| collection | DOAJ |
| description | In this paper we study the convergence of the approximate solutions for the following
first order problem
u′(t)=f(t,u(t));t∈[0,T],au(0)−bu(t0)=c,a,b≥0,t0∈(0,T].
Here f:I×ℝ→ℝ is such that ∂kf∂uk
exists and is a continuous function for some k≥1. Under some
additional conditions on ∂f∂u, we prove that it is possible to construct two sequences of approximate
solutions converging to a solution with rate of convergence of order k. |
| format | Article |
| id | doaj-art-43368c62ab014c89a4cfd448c3b700ed |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-43368c62ab014c89a4cfd448c3b700ed2025-02-03T01:04:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121349950510.1155/S0161171298000714Rapid convergence of approximate solutions for first order nonlinear boundary value problemsAlberto Cabada0Juan J. Nieto1Seppo Heikkilä2Departamento de Anàlise Matemhtica, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15706, SpainDepartamento de Anàlise Matemhtica, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15706, SpainDepartment of Mathematical Sciences, University of Oulu, Oulu 57 90570, FinlandIn this paper we study the convergence of the approximate solutions for the following first order problem u′(t)=f(t,u(t));t∈[0,T],au(0)−bu(t0)=c,a,b≥0,t0∈(0,T]. Here f:I×ℝ→ℝ is such that ∂kf∂uk exists and is a continuous function for some k≥1. Under some additional conditions on ∂f∂u, we prove that it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k.http://dx.doi.org/10.1155/S0161171298000714 |
| spellingShingle | Alberto Cabada Juan J. Nieto Seppo Heikkilä Rapid convergence of approximate solutions for first order nonlinear boundary value problems International Journal of Mathematics and Mathematical Sciences |
| title | Rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| title_full | Rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| title_fullStr | Rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| title_full_unstemmed | Rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| title_short | Rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| title_sort | rapid convergence of approximate solutions for first order nonlinear boundary value problems |
| url | http://dx.doi.org/10.1155/S0161171298000714 |
| work_keys_str_mv | AT albertocabada rapidconvergenceofapproximatesolutionsforfirstordernonlinearboundaryvalueproblems AT juanjnieto rapidconvergenceofapproximatesolutionsforfirstordernonlinearboundaryvalueproblems AT seppoheikkila rapidconvergenceofapproximatesolutionsforfirstordernonlinearboundaryvalueproblems |