Numerical solutions of nonlinear diferrential equations using operational matrix method

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This paper investigates a novel numerical scheme based on the operational matrix method and the second kind of Chebyshev polynomials to numerically solve some non-linear differential equations (NODEs). The proposed numerical method is given the truncated second-kind Chebyshev polynomial series solution of the relevant NODEs. The operational matrix method is applied to set a non-linear algebraic system to find such unknown series coefficients. Additionally, some inspections are revealed to analyze the convergency and error bounds of the method. Finally, eight problems are solved by the proposed method to show the effectiveness and trueness of the method.