TY - JOUR

T1 - Approximate Solution to a Multi-Point Boundary Value Problem Involving Nonlocal Integral Conditions by Reproducing Kernel Method

AU - Özen, Kemal

AU - Oruçoǧlu, Kamil

PY - 2013/9

Y1 - 2013/9

N2 - In this work, we investigate a sequence of approximations converging to the existing unique solution of a multi-point boundary value problem(BVP) given by a linear fourth-order ordinary differential equation with variable coeffcients involving nonlocal integral conditions by using reproducing kernel method(RKM). Obtaining the reproducing kernel of the reproducing kernel space by using the original conditions given directly by RKM may be troublesome and may introduce computational costs. Therefore, in these cases, initially considering more admissible conditions which will allow the reproducing kernel to be computed more easily than the original ones and then taking into account the original conditions lead us to satisfactory results. This analysis is illustrated by a numerical example. The results demonstrate that the method is still quite accurate and effective for the cases with both derivative and integral conditions even if the accuracy is less compared to the cases with just derivative conditions.

AB - In this work, we investigate a sequence of approximations converging to the existing unique solution of a multi-point boundary value problem(BVP) given by a linear fourth-order ordinary differential equation with variable coeffcients involving nonlocal integral conditions by using reproducing kernel method(RKM). Obtaining the reproducing kernel of the reproducing kernel space by using the original conditions given directly by RKM may be troublesome and may introduce computational costs. Therefore, in these cases, initially considering more admissible conditions which will allow the reproducing kernel to be computed more easily than the original ones and then taking into account the original conditions lead us to satisfactory results. This analysis is illustrated by a numerical example. The results demonstrate that the method is still quite accurate and effective for the cases with both derivative and integral conditions even if the accuracy is less compared to the cases with just derivative conditions.

KW - boundary value problem

KW - differential equation

KW - nonlocal boundary condition

KW - nonlocal integral condition

KW - reproducing kernel space

UR - http://www.scopus.com/inward/record.url?scp=84885122692&partnerID=8YFLogxK

U2 - 10.3846/13926292.2013.840867

DO - 10.3846/13926292.2013.840867

M3 - Article

AN - SCOPUS:84885122692

SN - 1392-6292

VL - 18

SP - 529

EP - 536

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

IS - 4

ER -