Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications
Sharma, V., Sharma, V., Singh, S. (2025). Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications. EKB Journal Management System, 13(1), 1-26. doi: 10.21608/ejmaa.2025.321121.1267
Vivek Kumar Sharma; Virendra Sharma; Sonoo Singh. "Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications". EKB Journal Management System, 13, 1, 2025, 1-26. doi: 10.21608/ejmaa.2025.321121.1267
Sharma, V., Sharma, V., Singh, S. (2025). 'Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications', EKB Journal Management System, 13(1), pp. 1-26. doi: 10.21608/ejmaa.2025.321121.1267
Sharma, V., Sharma, V., Singh, S. Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications. EKB Journal Management System, 2025; 13(1): 1-26. 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

Electronic Journal of Mathematical Analysis and Applications
Volume 13, Issue 1, 2025, Page 1-26  XML PDF (477.43 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2025.321121.1267
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Authors
Vivek Kumar Sharma email 1; Virendra Sharma1; Sonoo Singh2
1Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur
2Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University
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
Keywords
Extended sine-cosine Wavelet; Wavelet Approximation; functions of bounded derivatives
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