Title: Numerical approximation of Duffing equation using Hermite wavelet method

Authors: Jay Kishore Sahani; Pappu Kumar; Arvind Kumar; Satyendra Kumar

Addresses: Department of Mathematics, D.A.V. P.G. College, Siwan, Jai Prakash University, Chapra, India; Department of Mathematics, Jai Prakash University, Chapra, India; Department of Mathematics, Dyal Singh College, Delhi University, Delhi, India; Department of Mathematics, SSSVS Govt. P.G. College, Chunar, India ' Department of Mathematics, D.A.V. P.G. College, Siwan, Jai Prakash University, Chapra, India; Department of Mathematics, Jai Prakash University, Chapra, India; Department of Mathematics, Dyal Singh College, Delhi University, Delhi, India; Department of Mathematics, SSSVS Govt. P.G. College, Chunar, India ' Department of Mathematics, D.A.V. P.G. College, Siwan, Jai Prakash University, Chapra, India; Department of Mathematics, Jai Prakash University, Chapra, India; Department of Mathematics, Dyal Singh College, Delhi University, Delhi, India; Department of Mathematics, SSSVS Govt. P.G. College, Chunar, India ' Department of Mathematics, D.A.V. P.G. College, Siwan, Jai Prakash University, Chapra, India; Department of Mathematics, Jai Prakash University, Chapra, India; Department of Mathematics, Dyal Singh College, Delhi University, Delhi, India; Department of Mathematics, SSSVS Govt. P.G. College, Chunar, India

Abstract: This article presents an efficient technique based on Hermite wavelet for the numerical approximation of Duffing equation with and without damping force. The given equations are converted into a set of nonlinear algebraic equations with the help of truncated Hermite wavelet expansions and then find the values of the unknown vectors using Newton-Raphson method. The comparison has been made with analytical solution (if possible) and existing numerical solution to validate the Hermite wavelet solution (HWS). The HWS of Duffing equation in the absence of damping force shows excellent agreement with analytical solution and desired level of accuracy can be achieved by increasing number of collocation points. The HWS solution of Duffing equation in the presence of damping force has also been compared with existing solutions like the Taylor wavelet method, RK45 and others and was found more suitable, easy to implement and has a greater degree of accuracy with the same number of grid points.

Keywords: Hermite wavelet; operational matrix of integration; Duffing equation; nonlinearity.

DOI: 10.1504/IJMMNO.2025.146318

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.2, pp.168 - 184

Received: 29 Nov 2024
Accepted: 14 Mar 2025
Published online: 21 May 2025 *

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