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Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations

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  • Faheem, Mo
  • Raza, Akmal
  • Khan, Arshad

Abstract

In this paper, we introduce two different methods based on Gegenbauer wavelet and Bernoulli wavelet for the solution of neutral delay differential equations. These methods convert linear and nonlinear neutral delay differential equations into system of linear and nonlinear algebraic equations, respectively. After solving these equations, we get the approximate solutions. Here, we have used the Gegenbauer wavelet (for different values of μ) and Bernoulli wavelet and seen that both methods converge fast. We present six test problems consisting of five linear and one nonlinear, to illustrate the accuracy of present methods. Further, we compared our results with the results of existing methods present in the literature and have seen that our methods give more accurate results.

Suggested Citation

  • Faheem, Mo & Raza, Akmal & Khan, Arshad, 2021. "Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 72-92.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:72-92
    DOI: 10.1016/j.matcom.2020.08.018
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    References listed on IDEAS

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    1. Keshavarz, E. & Ordokhani, Y. & Razzaghi, M., 2019. "The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 83-98.
    2. Bashar Zogheib & Emran Tohidi & Stanford Shateyi, 2017. "Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-15, February.
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    Cited by:

    1. Kerr, Gilbert & González-Parra, Gilberto & Sherman, Michele, 2022. "A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Shahni, Julee & Singh, Randhir, 2022. "Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 430-444.
    3. Theodosiou, T.C., 2021. "Derivative-orthogonal non-uniform B-Spline wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 368-388.

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