Journal Article10.1515/IJNSNS-2020-0103
Wavelet collocation methods for solving neutral delay differential equations
Mo Faheem,Akmal Raza,Arshad Khan +2 more
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TL;DR: In this paper, the authors proposed wavelet based collocation methods for solving neutral delay differential equations numerically, and compared their results with Runge-Kutta-type methods by Wang et al.
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Abstract: In this paper we proposed wavelet based collocation methods for solving neutral delay differential equations. We use Legendre wavelet, Hermite wavelet, Chebyshev wavelet and Laguerre wavelet to solve the neutral delay differential equations numerically. We solve five linear and one nonlinear problem to demonstrate the accuracy of wavelet series solution. Wavelet series solution converges fast and gives more accurate results in comparison to other methods present in literature. We compare our results with Runge-Kutta-type methods by Wang et al. [1] and one-leg θ methods by Wang et al. [2] and observe that our results are more accurate.
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Citations
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Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method
TL;DR: Investigating the performance of the mathematical software program Maple and the programming language MATLAB when using these respective platforms to compute the method of steps (MoS) and the Laplace transform (LT) solutions for neutral and retarded linear delay differential equations (DDEs) found that, for linear non-neutral DDEs, MATLAB symbolic computations were faster than Maple.
Application of generalized Haar wavelet technique on simultaneous delay differential equations
Bipan Hazarika,Giriraj Methi,Rupal Aggarwal +2 more
TL;DR: This study applies the generalized Haar wavelet technique to solve simultaneous linear and nonlinear delay differential equations, demonstrating its accuracy and efficacy through numerical examples and error analysis, establishing its reliability and efficiency for solving delay differential equations.
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