Hashemi, Mir SajjadGholizadeh, LeilaAkgul, AliJarad, FahdForoutan, Mohammad Reza2024-02-092025-09-182024-02-092025-09-182022Foroutan, Mohammad Reza;...et.al. (2022). "A new application of the Legendre reproducing kernel method", AIMS Mathematics, Vol.7, No.6, pp.10671-10670.2473-6988https://doi.org/10.3934/math.2022594https://hdl.handle.net/20.500.12416/10446Hashemi, Mir Sajjad/0000-0002-5529-3125; Foroutan, Mohammadreza/0000-0002-7373-617XIn this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.eninfo:eu-repo/semantics/openAccessLegendre PolynomialsReproducing Kernel FunctionsApproximate SolutionConvergence AnalysisBoundary Value ProblemArticle10.3934/math.20225942-s2.0-85128149880