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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |