Comparison of Weighted Essentially non-Oscillatory Schemes for Long Time Marching of the Wave Equation

Document Type : Research Article

Author

School of Engineering Science, College of Engineering, University of Tehran

Abstract

Weighted essentially non-oscillatory schemes are among the most successful methods in numerical solutions to problems involving discontinuities. Since the accuracy of these schemes mostly depends on their weights, various methods have been proposed to improve the weights. Although some numerical experiments show that the introduced improvements have some drawbacks, there is no suitable criterion to show which of them is superior to the others. In this study, we introduce a new way of assessing the performance of weighted essentially non-oscillatory schemes: the schemes' performance in the long-time integration. This assessment can show the endurance of the scheme in preserving its maximum accuracy, which cannot be identified in a short time. Several methods from the literature are considered and is tested for the fifth, seventh, and ninth-order schemes. First, the third- and fourth-order Runge-Kutta schemes are used for the time integration. The results show the third- and fourth-order Runge-Kutta schemes have a very small effect on the results even for long-time integration. In contrast, increasing the order of the spatial accuracy has a significant effect on the accuracy of the results. Furthermore, it can be observed that the parameters that have negligible effects on the results in the short time have considerable effects on the accuracy of the results in the long time, and choosing a proper value for them is crucial to obtain reasonable accurate results.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 56, Issue 8
November 2025
Pages 1159-1182

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