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Published in:
2022 | OriginalPaper | Chapter
2. Novel Predictor-Corrector Formulations for Solving Nonlinear Initial Value Problems
Authors : Vahid Ahmadi Kalkhorani, Mohammad Mohammadi Aghdam
Published in: Nonlinear Approaches in Engineering Application
Publisher: Springer International Publishing
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Abstract
In this chapter, a novel predictor-corrector formulation is introduced based on the Bézier curve interpolation. The proposed formulation can be employed to determine numerical integration and solve nonlinear initial value problems with low computational cost while having larger stability region. The stability region of the method is examined in solving benchmark initial value problems, which showed a larger stability region both on the imaginary and real axis compared to some other well-known methods. The results of applying this formulation in solving Duffing and Van der Pol equations as numerical experiments showed that the proposed method is more stable and accurate for a wide range of step size compared to other well-known methods. Considering performance of the method in terms of accuracy, stability, and cost, it is expected that the method to be used is more complicated and applied nonlinear science and engineering problems.