An efficient numerical algorithm for solving delay differential equations based on second kind Chebyshev polynomials
This paper proposes a fast spectral technique based on second kind Chebyshev polynomials (SKCPs) to numerically solve delay differential equations (DDEs). First, we introduce some features of the SKCPs. Then, we use the operational matrices of coefficients, derivation, and stretch of the shifted SKC...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2025-04-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0271644 |
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| Summary: | This paper proposes a fast spectral technique based on second kind Chebyshev polynomials (SKCPs) to numerically solve delay differential equations (DDEs). First, we introduce some features of the SKCPs. Then, we use the operational matrices of coefficients, derivation, and stretch of the shifted SKCPs to convert DDEs into systems of algebraic equations. We show that these matrices are sparse, allowing for a fast implementation of the numerical calculations. A theoretical discussion about error estimation is conducted, and finally, numerical examples are given to highlight the accuracy and efficiency of the proposed method. |
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| ISSN: | 2158-3226 |