The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform
Yıl 2021,
Cilt: 6 Sayı: 3, 127 - 133, 30.12.2021
Sıdıka Şule Şener
,
Ercan Celık
,
Erhan Özdemir
Öz
In this paper, we apply ZZ- transform to solve linear Volterra integral equation of the first kind. The several examples solve by ZZ- Transform. This means that ZZ- transform is a powerful tool for solving linear Volterra integral equations of the first kind. The Convolution theorem for the ZZ- transform has been proved. ZZ- transform for the solution of linear Volterra integral equation of the first kind submitted in application section of this paper, some applications are given to demostrate the effectiveness of proposed scheme.
Kaynakça
- [1] Aggarwal S., Gupta AR., Singh DP., et al. Application of Laplace transform for solving population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9): 141-145, 2018.
- [2] Aggarwal S., Singh A., Kumar A., et al. Application of Laplace transform for solving improper integrals whose integrand consisting error function. Journal of Advanced Research in Applied Mathematics and Statistics, 4(2): 1-7, 2019.
- [3] Aboodh KS., Farah RA., Almardy IA et al. Solving delay differential equations by Aboodh transformation method. International Journal of Applied Mathematics & Statistical Sciences, 7(2): 55-64, 2018.
- [4] Eltayeb H., and Kilicman A., A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, Volume 4, no.22,1089-1098, 2010.
- [5] Tarig M. Elzaki, The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64, 2011.
- [6] Aggarwal S, Chauhan R, and Sharma N., A new application of Kamal transform for solving linear Volterra integral equations. International Journal of Latest Technology in Engineering, Management & Applied Science , 7(4): 138-140, 2018.
- [7] Mohand M. Abdelrahim M., and Tarig M. E., Elzaki Transform And Power Series Expansion On A Bulge Heaviside Step Function, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 11, Number 3, pp. 1179-1184, 2015.
- [8] Tarig M. E., and Salih M. E., On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18, 2011.
- [9] Najafi R., Küçük GD., and Çeli̇k E., Modified iteration method for solving fractional gas dynamics equation, Mathematical Methods in the Applied Sciences 40 (4), 939-946, 2017.
,
[10] Zain UI Abadin Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technology, 4(1), 1605-1611, 2016.
- [11] Sudhanshu A., and Nidhi S., Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation, Journal of Advanced Research in Applied Mathematics and Statistics, Volume 4, Issue 3&4, Pg. No. 16-23, 2019.
Yıl 2021,
Cilt: 6 Sayı: 3, 127 - 133, 30.12.2021
Sıdıka Şule Şener
,
Ercan Celık
,
Erhan Özdemir
Kaynakça
- [1] Aggarwal S., Gupta AR., Singh DP., et al. Application of Laplace transform for solving population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9): 141-145, 2018.
- [2] Aggarwal S., Singh A., Kumar A., et al. Application of Laplace transform for solving improper integrals whose integrand consisting error function. Journal of Advanced Research in Applied Mathematics and Statistics, 4(2): 1-7, 2019.
- [3] Aboodh KS., Farah RA., Almardy IA et al. Solving delay differential equations by Aboodh transformation method. International Journal of Applied Mathematics & Statistical Sciences, 7(2): 55-64, 2018.
- [4] Eltayeb H., and Kilicman A., A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, Volume 4, no.22,1089-1098, 2010.
- [5] Tarig M. Elzaki, The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64, 2011.
- [6] Aggarwal S, Chauhan R, and Sharma N., A new application of Kamal transform for solving linear Volterra integral equations. International Journal of Latest Technology in Engineering, Management & Applied Science , 7(4): 138-140, 2018.
- [7] Mohand M. Abdelrahim M., and Tarig M. E., Elzaki Transform And Power Series Expansion On A Bulge Heaviside Step Function, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 11, Number 3, pp. 1179-1184, 2015.
- [8] Tarig M. E., and Salih M. E., On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18, 2011.
- [9] Najafi R., Küçük GD., and Çeli̇k E., Modified iteration method for solving fractional gas dynamics equation, Mathematical Methods in the Applied Sciences 40 (4), 939-946, 2017.
,
[10] Zain UI Abadin Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technology, 4(1), 1605-1611, 2016.
- [11] Sudhanshu A., and Nidhi S., Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation, Journal of Advanced Research in Applied Mathematics and Statistics, Volume 4, Issue 3&4, Pg. No. 16-23, 2019.