Numerical Solution of A Class of Fourth-Order Differential Equations with Initial Conditions

Abstract: This paper presents the Runge-Kutta (RK4) method of order four for solving initial value problems of fourth-order ordinary differential equations. The proposed method is derived and is observed to be efficient and practically well-suited for handling high-order initial value problems. Two modal examples (linear and non-linear) are presented to demonstrate the reliability, accuracy and easy implementability of the method. The results obtained show a high level of accuracy when compared with the analytical solution.

Runge-Kutta, ordinary differential equations, initial value problem, finite difference method, numerical approximation

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