A Comparative Study Between ADM and MDM for a System of Volterra Integral Equation
DOI:
https://doi.org/10.15642/mantik.2021.7.2.140-146Keywords:
System of Volterra Integral Equations, Adomain decomposition method, Modified decomposition methodAbstract
In this paper, a comparative study between Adomain decomposition method (ADM) and Modified decomposition method (MDM) for a system of volterra integral equation. From the illustrate examples it is observed that the exact solution is smaller in both methods, the modified decomposition method is more proficient than its traditional ones it is less complicated, needs less time to get to the solution and most importantly the exact solution is achieved in two iterations.
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S. S. Ahmed, Numerical solution for Volterra-Fredholm integral equation of the second kind by using least squares technique. Iraqi Journal of Science 52, no. 4 (2011): 504-512.
M. U. S. A. Aigo, On the numerical approximation of Volterra integral equations of the second kind using quadrature rules. International Journal of Advanced Scientific and Technical Research 1, no. 3 (2013): 558-564.
A. M. Wazwaz, A First course in Integral Equations, World Scientific Publishing, London,(2015).
J. Biazar and M. Pourabd, A Maple Program for Solving Systems of Linear and Nonlinear Integral Equations by Adomian Decomposition Method. Int. J. Contemp. Math. Sciences 2, no. 29 (2007): 1425-1432.
H. Brunner, E. Hairer and S. P. Njersett, Runge-Kutta theory for Volterra integral equations of the second kind. MATHEMATICS of computation 39, no. 159 (1982): 147-163.
W. Hackbusch, Integral Equations: Theory and Numerical Treatment, Birkhauser Verlag, Basel, (1995).
A. Isaacson and M. Kirby, Numerical solution of linear Volterra integral equations of the second kind with sharp gradients. Journal of computational and applied mathematics 235, no. 14 (2011): 4283-4301.
M. Mustafa, Numerical solution of volterra integral equations with Delay using Block methods. AL-Fatih journal 36 (2008).
M. M. Rahman, Numerical Solution s of Volterra Integral Equations Using Calerkin method with Hernite polynomials, pure and Appl. Math.,(2013).
Md A. Rahman, Md S. Islam, and M. M. Alam, Numerical solutions of Volterra integral equations using Laguerre polynomials. Journal of scientific research 4, no. 2 (2012): 357-357
A. G. Ramm, A collocation method for solving integral equations. International Journal of Computing Science and Mathematics 2, no. 3 (2009): 222-228.
J. Rashidinia, E. Najafi and A. Arzhang, An iterative scheme for numerical solution of Volterra integral equations using collocation method and Chebyshev polynomials, Rashidinia et al. Mathematical Sciences 2012.
J. Saeri-Nadja and M. Heidari, Solving linear integral equations of the second kind with repeated modified trapezoid quadrature method. Appl . Math. Comput., 189 (2007), 980-985.
A. Tahmasbi, A new approach to the numerical solution of linear Volterra integral equations of the second kind. Int. J. Contemp. Math. Sciences 3, no. 32 (2008): 1607-1610.
M. S. Islam and Md. A. Rahman, Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials. International Journal of Computers & Technology 11 (2013): 2910-2920.
A. M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications (2011). Higher Education, Springer, Beijing, Berlin.
G. Adomian, Nonlinear stochastic systems and Applications to Physics, Kluwer,(1989).
G. Adomian, G.E. Adomian, A global method for solution of complex systems, Math. Model, 5 (1984) 521-568.
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