Postprocessing technique of the discontinuous Galerkin method for solving delay differential equations

We introduce an innovative postprocessing technique aimed at refining the accuracy of the discontinuous Galerkin method for solving linear delay differential equations (DDEs) with vanishing delays. The fundamental idea behind this postprocessing technique is to enhance the discontinuous Galerkin sol...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2024, Vol.70 (4), p.3603-3630
Main Authors: Tu, Qunying, Li, Zhe, Yi, Lijun
Format: Article
Language:English
Subjects:
Accuracy
Computational Mathematics and Numerical Analysis
Convergence
Differential equations
Galerkin method
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical analysis
Original Research
Polynomials
Theory of Computation
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Summary:We introduce an innovative postprocessing technique aimed at refining the accuracy of the discontinuous Galerkin method for solving linear delay differential equations (DDEs) with vanishing delays. The fundamental idea behind this postprocessing technique is to enhance the discontinuous Galerkin solution of degree k by incorporating a generalized Jacobi polynomial of degree k + 1 . We demonstrate that this postprocessing step enhances convergence by one order under the L ∞ -norm. Moreover, we apply this technique to both nonlinear DDEs with vanishing delays and linear DDEs with non-vanishing delays. We further validated the theoretical results through a series of numerical examples.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02114-3