A New Decomposition Method for Integro-Differential Equations
Abstract
This present study developed a new Modified Adomian Decomposition Method (MADM) for integro-differential equations. The modification was carried out by decomposing the source term function into series. The terms in the series were then selected in pairs to form the initials for the prevailing approximation. The newly modified Adomian decomposition method (MADM) accelerates the convergence of the solution faster than the Standard Adomian Decomposition Method (SADM). This study recommends the use of the MADM for solving integro-differential equations.
Keywords
Adomian Polynomials, Integro-differential equations, Taylor Series
References
- [1] Dzhumabaev D.S., New general solutions to linear Fredholm integro-differential equations and their applications on solving the boundary value problems, Journal of Computational and Applied Mathematics, 327 (2018) 79-108.
- [2] Fairbairn A.I., Kelmanson, M.A., Error analysis of a spectrally accurate Volterra-transformation method for solving 1-D Fredholm integro-differential equations, International Journal of Mechanical Sciences, 144 (2018) 382-391.
- [3] Hendi F.A., Al-Qarni M.M., The variational Adomian decomposition method for solving nonlinear two- dimensional Volterra-Fredholm integro-differential equation, Journal of King Saud University – Science, 31(1) (2017) 110-113.
- [4] Kürkçü Ö.K., Aslan, E., Sezer, M., A novel collocation method based on residual error analysis for solving integro-differential equations using Hybrid Dickson and Taylor polynomials, Sains Malaysiana, 46(2) (2017) 335-347.
- [5] Rahimkhani P., Ordokhani Y., Babolian E., Fractional-order Bernoulli functions and their applications in solving fractional Fredholem-Volterra integro-differential equations, Applied Numerical Mathematics, 122 (2017) 66-81.
- [6] Rohaninasab N., Maleknejad K., Ezzati R., Numerical solution of high-order Volterra-Fredholm integro-differential equations by using Legendre collocation method, Applied Mathematics and Computation, 328 (2018) 171-188.
- [7] Yüzbaşı Ş., Karaçayır M., A Galerkin-like scheme to solve two-dimensional telegraph equation using collocation points in initial and boundary conditions. Computers and Mathematics with Applications 74 (2017) 3242-3249.
- [8] Abbas S., Benchohra M., N’Guerekata G.M., Advanced Fractional Differential and Integral Equations. New York: Nova Science Publishers, (2015).
- [9] Alkan S., Hatipoglu V.F. Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order, Tbilisi Mathematical Journal, 10(2) (2017) 1-13.
- [10] Hamoud A.A., & Ghadle K.P., The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Problemy Analiza Issues of Analysis, 7(25) (2018a) 41-58.