An ‎E‎ffective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument

Subject Areas : International Journal of Industrial Mathematics

M.  Khaleghi ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
E.  Babolian ² (Faculty of Mathematical Sciences and Computer, Kharazmy University, Tehran, Iran.)
S.  Abbasbandy ³ (Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.)

Received: 2017-08-13 Accepted : 2018-05-18 Published : 2019-12-01

Keywords: Two-point boundary value problem, Deviating argument, Chebyshev reproducing kernel method, Polynomial reproducing kernel, Chebyshev polynomials,

Abstract :

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some numerical examples.