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A Numerical Approach Based on Modified Lucas Wavelets for Functional Variational Problems Through Integral Operational Matrix

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Abstract

The present work introduces an approximated numerical technique for functional variational problems (FVPs) with mixed boundary conditions which are based on the integral operational matrix (IOM) for modified Lucas wavelets. Both, its algorithm and pseudo code are discussed. In this approach, the functional variational problems are transformed into the most familiar algebraic system with the help of the integral operational matrix and the Lagrange multipliers technique. The introduced numerical approach has been tested on some experimental applications, and found that the proposed approach was more suitable for the numerical solutions of FVPs with higher accuracy. The performance of the present approach is better than the performance of existing methods and the techniques available in the literature. Hence, the modified Lucas wavelets provide an approximate solution that is very close to the exact solution of FVPs.

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Acknowledgements

The authors express their heartfelt gratitude to Dr. K. Raju, Professor, Department of Mechanical Engineering, St. Joseph Engineering College, Mangaluru, India for his timely help in editing the manuscript.

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  1. Department of Mathematics and Statistics, Gurukula Kangri (Deemed to Be University), Haridwar, Uttarakhand, 249404, India

    Ankit Kumar & Sag Ram Verma

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Kumar, A., Verma, S.R. A Numerical Approach Based on Modified Lucas Wavelets for Functional Variational Problems Through Integral Operational Matrix. Int. J. Appl. Comput. Math 9, 138 (2023). https://doi.org/10.1007/s40819-023-01616-1

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