Computational Numerical Method for Direct Solutions of Second Order Oscillatory Problems
DOI:
https://doi.org/10.62054/ijdm/0302.07Abstract
This study presents a Computational Numerical Method (CNM) for directly solving second-order oscillatory initial value problems without reducing them to systems of first-order differential equations. The CNM is derived by constructing a power series polynomial as a basis function, which is differentiated and collocated at some points to form a continuous hybrid linear multistep method. The method’s properties, including order, error constant, consistency, zero-stability, convergence and region of absolute stability, are rigorously analyzed to ensure accuracy and reliability. Numerical simulations are conducted on physical and engineering problems, including second-order cooling oscillatory differential equation, simple harmonic motion and Stiefel linear oscillatory differential equations. The results demonstrate near-perfect agreement between analytical and numerical solutions confirmed that, the CNM is efficient and effectiveness in modeling oscillatory differential equations in dynamic systems. The results indicate that the CNM is a robust tool for accurately simulation of second-order oscillatory differential equations.
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