Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications

Sharma, Vivek Kumar; Sharma, Virendra; Singh, Sonoo

doi:10.21608/ejmaa.2025.321121.1267

Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications

Document Type : Regular research papers

Authors

¹ Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur

² Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University

10.21608/ejmaa.2025.321121.1267

Abstract

Wavelets are very powerful tools for solving certain problems in mathematical analysis. Due
to their well localized behavior, wavelets are very useful for developing new numerical methods
and due to this reason researchers are trying to develop new numerical techniques using different
wavelets. Keeping it mind, In this paper, we have introduced the extended sine-cosine wavelet
and it is used to find the approximations of a functions having bounded derivatives upto the
second order. Next, we have calculated the operational matrix of integration for different values
of parameter µ using these approximations. Then, we have applied these approximations and
operational matrices to find the solutions of some differential and integral equations. Lastly, the
comparison between exact solution and approximate solutions have been discussed to show the
usefulness of the method. From the tables 1 and 3, we see that as we increase the value of µ,
the approximate solution becomes closer to the exact solution which shows the validity of the
proposed method

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