Özet:

We propose and present a self-starting numerical approximation with a higher order of accuracy for direct solution of a special fourth-order ordinary differential equation (ODE) using a Hybrid Linear Multistep Method (HLMM). The technique utilizes the collocation and interpolation approach with six-step numbers and two off-step points using power series as the basis function. Error constants and basic properties proved the convergence of the method. Numerical experiments involving both linear, nonlinear, and linear systems of fourth-order initial value problems appearing in modeling of physical phenomenon from various areas of applied sciences were used to demonstrate the effectiveness and efficiency of the proposed method. The results revealed that the proposed method is an excellent choice for approximating general fourth-order ODE and shows the impact of choices of step sizes in the numerical solution of the problem considered. In addition, the proposed HLMM outperformed existing methods in the literature in terms of accuracy

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