Chebyshev solution for neutral delay differential equations

Hussien, M. A.

doi:10.1080/00207169908804893

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“…They applied several examples to check the order of convergence of these methods. Hussien [7] suggested a numerical scheme based on the Chebyshev series to approximate the numerical solution of NDDEs, which is applicable to neutral and advanced DDEs with single or multiple delay terms. Li and Zhang [8] reviewed discontinuous Galerkin methods $L_{\infty}$ error estimates, for the analytical solution of DDEs.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis and Numerical Solution of Linear and Nonlinear Neutral Delay Differential Equations

AMIN,

SHER,

ALI

et al. 2024

J. Sci. Arts

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In this paper, a collocation method based on the Haar wavelet is presented for the solution of both linear and nonlinear first-order neutral delay differential equations. The Haar functions are used to approximate the first-order derivative, and the approximate solution is obtained by using initial condition and integration. Some examples from the literature are used to test the suggested method efficiency and applicability. A comparison of exact and approximate solutions is given in figures for different numbers of collocation points. The root mean square and maximum absolute errors are calculated for different numbers of collocation points. The rate of convergence is calculated which is approximately equal to 2. The comparison of the present method with the other numerical methods is also given. The results demonstrate that the Haar wavelet collocation method is simple and effective for solving first-order linear and nonlinear neutral delay differential equations.

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Section: Introductionmentioning

confidence: 99%