An efficient fourth-order method for direct integration of second-order ordinary differential equations
Keywords:
Continuous linear multistep method, Zero stability, CollocationAbstract
This paper presents a novel fourth-order block method for the direct integration of second-order differential equations. The method is derived from a basis function that combines a third-order polynomial with the sum of sine and cosine functions. By leveraging this unique basis function, the proposed method maintains computational efficiency while achieving fourth-order accuracy. It outlines the method's derivation and analyzes its stability and accuracy properties. Numerical experiments demonstrate its effectiveness and efficiency compared to existing techniques. The results indicate that the proposed fourth-order block method offers signicant advantages in accuracy and computational cost, making it promising for directly integrating
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Copyright (c) 2024 Opeyemi Enoch, Emmanuel Adeyefa, Catherine Alakofa
This work is licensed under a Creative Commons Attribution 4.0 International License.
