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<p>In this paper, sixth-kind Chebyshev wavelet is considered. The moduli of continuity of a functions in Hölder’s class by sixth-kind Chebyshev wavelets have been determined. The current study examines the solution of Rayleigh, Van der Pol and Duffing differential equations. The sixth-kind Chebyshev wavelets collocation approach is introduced to solve the Rayleigh differential equation, Van der Pol differential equation, and Duffing differential equation. The solution obtained by sixth-kind Chebyshev wavelets method are compared with solution obtained by Algebraic method (AGM) and ODE45 method. The proposed algorithms have provided accurate results, even using few terms of the wavelet expansion. The numerical results demonstrate that our method is simply applicable, efficient, powerful and very precise at the small number of basis functions.</p>

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Moduli of continuity of functions in H\(\ddot{\text {o}}\)lder’s class and solution of Rayleigh, Van der Pol and Duffing equations by sixth-kind Chebyshev wavelets

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Shyam Lal,
  • Deepak Kumar Singh

摘要

In this paper, sixth-kind Chebyshev wavelet is considered. The moduli of continuity of a functions in Hölder’s class by sixth-kind Chebyshev wavelets have been determined. The current study examines the solution of Rayleigh, Van der Pol and Duffing differential equations. The sixth-kind Chebyshev wavelets collocation approach is introduced to solve the Rayleigh differential equation, Van der Pol differential equation, and Duffing differential equation. The solution obtained by sixth-kind Chebyshev wavelets method are compared with solution obtained by Algebraic method (AGM) and ODE45 method. The proposed algorithms have provided accurate results, even using few terms of the wavelet expansion. The numerical results demonstrate that our method is simply applicable, efficient, powerful and very precise at the small number of basis functions.