Exact Solution of Non-Linear Volterra Integral Equation of First Kind Using Rishi Transform
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1Sudhanshu Aggarwal*, 2Rishi Kumar, 3Jyotsna Chandel
Bulletin of Pure and Applied Sciences
Section – E – Mathematics & Statistics
Vol. 41E, No.2, July-December 2022.P.159-166
DOI: 10.5958/2320-3226.2022.00022.4.
Original Article
Description
Description
Exact Solution of Non-Linear Volterra Integral Equation of First Kind Using Rishi Transform
1Sudhanshu Aggarwal*, 2Rishi Kumar, 3Jyotsna Chandel
Author’s Affiliation:
1Assistant Professor, Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur-273402, Uttar Pradesh, India
E-mail: sudhanshu30187@gmail.com
2Research Scholar, Department of Mathematics, D.S. College, Aligarh (Dr. Bhimrao Ambedkar University, Agra), Uttar Pradesh 202001, India
E-mail: rishi.saraswat1987@gmail.com
3Associate Professor, Department of Mathematics, D.S. College, Aligarh (Dr. Bhimrao Ambedkar University, Agra), Uttar Pradesh 202001, India
E-mail: jyotsnaraghuvanshi5@gmail.com
*Corresponding Author: Sudhanshu Aggarwal, Assistant Professor, Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur-273402, Uttar Pradesh, India
E-mail: sudhanshu30187@gmail.com
How to cite this article: Aggarwal S., Kumar R., Chandel J. (2022). Exact Solution of Non-Linear Volterra Integral Equation of First Kind Using Rishi Transform. Bull. Pure Appl. Sci. Sect. E Math. Stat. 41E(2), 159-166.
Received on 12.09.2022/ Revised on 20.11.2022/ Accepted on 30.11.2022
Online First Published on Dec 15, 2022 at https://www.bpasjournals.com/
Abstract
The problems of Engineering and Science can easily represent by developing their mathematical models in the terms of integral equations. Various analytical and numerical methods are available that can be used for solving integral equations of different kinds. In this paper, authors have considered recently developed integral transform “Rishi Transform” for obtaining the exact solution of non-linear Volterra integral equation of first kind (NLVIEFK). Four numerical problems have considered for demonstrating the complete procedure of determining the exact solution. Results of these problems depict that Rishi transform is very effective integral transform and it provides the exact solution of NLVIEFK without doing complicated calculation work.
KEYWORDS: Analytical Solution; Rishi Transform; Inverse Rishi Transform; Convolution; Volterra Integral Equation.
Mathematics Subject Classification: 35A22; 44A05; 44A35; 45D05; 45G10
