Foroutan, Mohammad RezaHashemi, Mir SajjadGholizadeh, LeilaAkgül, AliJarad, Fahd2024-02-092024-02-092022Foroutan, Mohammad Reza;...et.al. (2022). "A new application of the Legendre reproducing kernel method", AIMS Mathematics, Vol.7, No.6, pp.10671-10670.24736988http://hdl.handle.net/20.500.12416/7146n 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/openAccessApproximate SolutionBoundary Value ProblemConvergence AnalysisLegendre PolynomialsReproducing Kernel FunctionsArticle76106511067010.3934/math.2022594