Foroutan, Mohammad RezaHashemi, Mir SajjadGholizadeh, LeilaAkgul, AliJarad, Fahd2024-12-242024-12-2420222473-6988https://doi.org/10.3934/math.2022594https://hdl.handle.net/20.500.12604/8385In 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 problemArticle761065110670Q1WOS:000782283500002Q12-s2.0-8512814988010.3934/math.2022594