A new approach for Solving a nonlinear system of second-order BVPs

In this paper, we introduce a new approach based on the Reproducing Kernel Method (RKM) for solving a nonlinear system of second-order Boundary Value Problems (BVPs) without the Gram-Schmidt orthogonalization process. What motivates us to use the RKM without the Gram-Schmidt orthogonalization proces...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 29; no. 4; pp. 669 - 683
Main Authors Amoozad, Taher, Abbasbandy, Saeid, Allahviranloo, Tofigh, Rostamy Malkhalifeh, Mohsen
Format Journal Article
LanguageEnglish
Published Vilnius Gediminas Technical University 11.10.2024
Subjects
convergence analysis
error analysis
reproducing kernel method
system of second-order boundary value problem
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Summary:In this paper, we introduce a new approach based on the Reproducing Kernel Method (RKM) for solving a nonlinear system of second-order Boundary Value Problems (BVPs) without the Gram-Schmidt orthogonalization process. What motivates us to use the RKM without the Gram-Schmidt orthogonalization process is its easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy. Finally, the compatibility of numerical results and theorems demonstrates that the Present method is effective.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2024.19217