On the construction of the approximate solution of a special type integral boundary value problem

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Abstract

We consider the integral boundary value problem (BVP) for a certain class of non-linear system of ordinary differential equations of the form (Formula Presented) where (Formula Presented) and t ∈ [0,T], x ∈ ℝn, f : [0,T] × D → ℝ n and k : [0-T] × → ℝ n are continuous vector functions, D ⊂ ℝn is a closed and bounded domain, A, C and d are arbitrary matrices and vector with real components, det C ≠ 0. We give a new approach for studying this problem, namely by using an appropriate parametrization technique the original BVP is reduced to the equivalent parametrized two-point one with linear restrictions without integral term. To study the transformed problem we use a method based upon a special type of successive approximations constructed analytically.

Original languageEnglish
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2016
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Integral boundary value problems
  • Numerical–analytic technique
  • Parametrization
  • Successive approximations

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