Solution and Numerical Comparison of Linear Volterra Integral Equations of the Second Kind
Yakubu G, Ahmed I, Ali Mustapha PhD, Modu Muhammed
Abstract
This paper evaluates the efficacy of the Variational Iteration Method (VIM) and the Adomian Decomposition Method (ADM) in solving linear Volterra integral equations. A series solution method is employed to obtain the exact solution. Furthermore, approximate solutions generated by VIM and ADM are then compared with the exact solutions through numerical computations. The findings reveal that both methods converge rapidly with high accuracy, demonstrating their effectiveness and computational efficiency for the class of problems considered.
Keywords
Variational Iteration Method
Series Solution Method
Adomian Decomposition
References
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Wazwaz. A. M. (2014). A comparison between the variational iteration method and
Adomian decomposition method. Journal of Computational and Applied Mathematics 207
(2007) 129–136
Fawziah, M.,A., & Kirtiwant ,P.G., (2019). The numerical solution of linear and non linear
voltera integral equation of the second kind using variational iteration method.Acta
university mathise beilie, services mathematics 27(2019) 32-42.
Mechee, M. S., Al Ramahi, A. M., & Kadum, R. M. (2016). Applications of variational
iteration method for solving a class of Volterra integral equations. Journal of Babylon
University/Pure and Applied Sciences, 24(9), 2397–2404.
Abdirashidov, A., Usanov, F., Kasimova, F., & Ismoilov, X. (2020). Application of
approximate
methods
for
solving
higher
order
Voltera
integro-differential
equations. Theoretical
&
Applied
Science,
(87),
250–256.
https://doi.org/10.15863/TAS.2020.07.87.51
Abdul-majid and Khuri (2014). the variational iteration method for solving the voltera
integro differential forms of Lane-Emden and the Emden-fowler problems with initial
boundary value conditions.
Sheth, S. S., & Singh, T. (2019). An analytical approximate solution of linear, system of
linear and non linear Volterra integral equations using variational iteration method.
In Proceedings of the International Conference on Advancements in Computing &
Management (ICACM).
Wazwaz, A. M. (2010). The variational iteration method for solving linear and nonlinear
Volterra integral and integro-differential equations. International Journal of Computer
Mathematics, 87(5), 1131-1141.
Wazwaz. A. M. (2014). A comparison between the variational iteration method and
Adomian decomposition method. Journal of Computational and Applied Mathematics 207
(2007) 129–136
Fawziah, M.,A., & Kirtiwant ,P.G., (2019). The numerical solution of linear and non linear
voltera integral equation of the second kind using variational iteration method.Acta
university mathise beilie, services mathematics 27(2019) 32-42.
Mechee, M. S., Al Ramahi, A. M., & Kadum, R. M. (2016). Applications of variational
iteration method for solving a class of Volterra integral equations. Journal of Babylon
University/Pure and Applied Sciences, 24(9), 2397–2404.
Abdirashidov, A., Usanov, F., Kasimova, F., & Ismoilov, X. (2020). Application of
approximate
methods
for
solving
higher
order
Voltera
integro-differential
equations. Theoretical
&
Applied
Science,
(87),
250–256.
https://doi.org/10.15863/TAS.2020.07.87.51
Abdul-majid and Khuri (2014). the variational iteration method for solving the voltera
integro differential forms of Lane-Emden and the Emden-fowler problems with initial
boundary value conditions.
Sheth, S. S., & Singh, T. (2019). An analytical approximate solution of linear, system of
linear and non linear Volterra integral equations using variational iteration method.
In Proceedings of the International Conference on Advancements in Computing &
Management (ICACM).
Wazwaz, A. M. (2010). The variational iteration method for solving linear and nonlinear
Volterra integral and integro-differential equations. International Journal of Computer
Mathematics, 87(5), 1131-1141.
