Rapid convergence of approximate solutions for first order nonlinear boundary value problems

Alberto Cabada, Juan J. Nieto and Seppo Heikkilä

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-7

Abstract:

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 ] , a u ( 0 ) − b u ( t 0 ) = c , a , b ≥ 0 , t 0 ∈ ( 0 , T ] . Here f : I × ℝ → ℝ is such that ∂ k f ∂ u k 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 .

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:387956

DOI: 10.1155/S0161171298000714

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