Application of Linear Block Methods for Solving Higher-Order Initial Value Problems
Keywords:
Consistency, Convergence, Computational Efficiency, Higher-Order Oscillatory, Linear Block Approach, Numerical MethodsAbstract
This research investigates the challenges of solving higher-order oscillatory ordinary differential equations (ODEs), which frequently arise in various scientific and engineering applications. Many of these problems lack explicit solutions, necessitating the development of robust numerical methods. This study proposes a novel approach to solving such equations by employing a two-step linear multistep method specifically designed for directly addressing higher-order oscillatory differential equations. Key numerical properties, including consistency, zero stability, convergence, and linear stability, are thoroughly analyzed to validate the effectiveness of the proposed scheme. The effectiveness of the new method is illustrated through a series of numerical examples, highlighting its
accuracy and efficiency compared to existing methods in the literature. The results demonstrate that the proposed method outperforms traditional techniques in solving complex oscillatory problems, providing reliable and computationally efficient solutions suitable for real-world applications.
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