과제정보
The authors are grateful to the referees and the editor for their valuable suggestions and remarks that definitely improved the paper. The authors would like to thank the Integral University, Lucknow, India, for providing the manuscript number IU/R&D/2023-MCN0002260 to the present work.
참고문헌
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Boston, 1994.
- W. Chen, Z. Lu, An Algorithm for Adomian Decomposition Method, Applied Mathematics and Computation 159 (2004), 221-235.
- D.J. Evans, K.R. Raslan, The Adomian Decomposition Method for Solving Delay Differential Equation, International Journal of Computer Mathematics 82 (2005), 49-54.
- A.U. Keskin, Boundary Value Problems for Engineers with MATLAB Solutions, chapter Adomian Decomposition Method (ADM), Springer Cham, (2019) 311-359.
- E.U. Haq, Q.M.U. Hassan, J. Ahmad, K. Ehsan, Fuzzy solution of system of fuzzy fractional problems using a reliable method, Alexandria Engineering Journal 61 (2022), 3051-3058.
- N.H. Sweilam, Fourth order integro-differential equations using variational iteration method, Computers & Mathematics with Applications 54 (2007), 1086-1091.
- N. Khan, Q.M.U. Hassan, E.U. Haq, M.Y. Khan, K. Ayub, J. Ayub, Analytical Technique With Lagrange Multiplier For Solving Specific Nonlinear Differential Equations, Journal of Science and Arts 21 (2021), 5-14.
- Kumar, Pramod, Numerical Solutions of Linear Fredholm Integro-Differential Equations by Non-Standard Finite Difference Method, Applications and Applied Mathematics 10 (2015), 1019-1025.
- N. Ahmad, B. Singh, Numerical solution of Integral Equation by Using New Modified Adomian Decomposition Method and Newton Raphson Method, International Journal of Innovative Technology and Exploring Engineering (IJITEE) 10 (2021), 5-8.
- Ahmad N., Singh B., Study of Numerical solution of nonlinear Integral Equations by Using Adomian Decomposition Method and HE's Polynomial, Journal of Mathematical Control Science and Applications 6 (2), (2020) 93-95.
- N. Anjum, J.H. He, Laplace transform: Making the variational iteration method easier, Applied Mathematics Letters 92 (2019), 134-138.
- N. Ahmad, B. Singh, Numerical solution of Integral Equation by Using Galerkin Method with Hermite, Chebyshev and Orthogonal Polynomials, Journal of Science and Arts 50 (2020), 35-42.
- S. Abbasbandy and S. Elyas, Series Solution of the System of Integro-Differential Equations, A Journal of Physical Sciences 64a (2009), 811-818.
- A. Rani, M. Saeed, Q.M. Ul-Hassan, M. Ashraf, M.Y. Khan, K. Ayub, Solving system of differential equations of fractional order by Homotopy analysis method, Journal of Science and Arts 17 (2017), 457-468.
- A.A. Soliman, Exact solutions of KdV-Burgers' equation by Exp-function method, Chaos, Solitons & Fractals 41 (2009), 1034-1039.
- M. Senthilvelan, On the extended applications of Homogenous Balance Method, Applied Mathematics and Computation 123 (2001), 381-388.
- W. Majid Abdul, A Reliable Modification of Adomian Decomposition Method, Applied Mathematics and Computation 102 (1999), 77-86.
- A.W. Majid, S.M. El-Sayed, A New Modification of the Adomian Decomposition Method for Linear and Nonlinear Operators, Applied Mathematics and Computation 122 (2001), 393-405.
- W. Majid, Abdul, Linear and Nonlinear Integral Equations, Higher Education Press, Beijing, 2011.
- L. Peter, Analytical and Numerical Methods for Volterra Equations, Studies in Applied Mathematics, SIAM, Philadelphia, 1985.
- M.G. Amani, A.M. Dalal, Z.B. Badreeh, Numerical Solution of Volterra Integral Equation of Second Kind Using Implicit Trapezoidal, Journal of Advances in Mathematics 8 (2014), 1540-1553.
- A.M. Dalal, The Adomian Decomposition Method of Fredholm Integral Equation of the Second Kind Using Maple, Journal of Advances in Mathematics 9 (2014), 1868-1875.
- M. Malaikah Hunida , The Adomian Decomposition Method for Solving Volterra-Fredholm Integral Equation Using Maple, Applied Mathematics 11 (2020), 779-787.
- A. Ameera, M Dalal, A. Hashim, Adomian Decomposition Method for Solving Boussinesq Equations Using Maple, Applied Mathematics 14 (2023), 121-129.
- A.M. Dalal, Application of Adomian Decomposition Method for Solving of Fredholm Integral Equation of the Second Kind, European Journal of Science and Engineering 9 (2014), 1-9.
- A.M. Dalal, Adomian Decomposition Method for Solving of Fredholm Integral Equation of the Second Kind Using MATLAB, International Journal of GEOMATE 11 (2016), 2830-2833.
- A.M. Dalal, M.M. H., Numerical Solution of System of Three Nonlinear Volterra Integral Equation Using Implicit Trapezoidal, Journal of Mathematics Research 10 (2018), 44-58.
- A.M. Wazwaz, A First Course in Integral Equations, World Scientific, 1997.
- N. Ahmad, B. Singh, Numerical Solution of Volterra Nonlinear Integral Equation by using Laplace Adomian Decomposition Method, International Journal of Applied Mathematics 35 (2022), 39-48.
- A. Asiya, N. Ahmad, Numerical Accuracy of Fredholm linear Integro-differential equations by using Adomian Decomposition Method, Modified Adomian Decomposition Method and Variational Iteration Method, Journal of Science and Arts 23 (2023), 625-638.
- A. Asiya, N. Ahmad, Numerical Accuracy of Fredholm Integro-differential equations by using Adomian Decomposition Method and Modified Adomian Decomposition Method, Bull. Cal. Math. Soc. 115 (2023), 567-578.
- D.I. Lanlege, F.M. Edibo and S.O. Momoh, Solution of Fredholm Integro-Differential Equation by Variational Iteration Method, FUDMA Journal of Sciences (FJS) 7 (2023), 1-8.
- A. Asiya, N. Ahmad and D. Farah, Application of The Direct Computation Method for Solving a General Fredholm Integro-Differential Equations, Global and Stochastic Analysis 11 (2024), 65-74.
- A. Asiya, N. Ahmad, Numerical Solution for nonlinear Volterra-Fredholm Integro-Differential Equations using Adomian and Modified Adomian Decomposition Method, Transylvanian Review 31 (2023), 16321-16327.