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    A new application of the Legendre reproducing kernel method
    (Amer Inst Mathematical Sciences-Aims, 2022) Foroutan, Mohammad Reza; Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd
    In 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.