1Research Scholar, USBAS, GGSIPU, Delhi, India
2Fellow of Institute of Mathematics & Applications (UK), Professor of Mathematics, Head, Non-Linear Dynamics Research Lab, University School of Basic and Applied Sciences(USBAS), Guru Gobind Singh Indraprastha University (GGSIPU), Dwarka, Delhi, India
*Corresponding author E-mail: vini.sangwan14@gmail.com
Online Published on 11 November, 2023.
This paper introduces a solution to special differential equations using wavelets and operational matrices. The solution involves approximating the solution function within the wavelet space, specifically in the Hermite space. Additionally, we employ the previously described Operational Matrix of Integration (OMI) in conjunction with the collocation method by discretizing the given problem at collocation points. To convert the differential equations into simultaneous algebraic equations, we harness various properties of wavelets. The applicability of the proposed technique is demonstrated through illustrative numerical problems. The results obtained using this approach are favorable when compared to exact solutions and associated errors, validating its effectiveness.
Wavelets, Differential Equations, Hermite Space, Operational Matrix, Collocation Method, Collocation Points, Operational Matrix of Integration (OMI), Algebraic Equations
