On the Solution of Volterra Integro-differential Equations using a Modified Adomian Decomposition Method

Kabiru Oyeleye Kareem; Morufu Olayiwola; Oladapo Asimiyu; Yunus Akeem; Kamilu Adedokun; Ismail Alaje

doi:10.34312/jjom.v5i2.19029

On the Solution of Volterra Integro-differential Equations using a Modified Adomian Decomposition Method

Kabiru Oyeleye Kareem, Morufu Olayiwola, Oladapo Asimiyu, Yunus Akeem, Kamilu Adedokun, Ismail Alaje

Abstract

The Adomian decomposition method’s effectiveness has been demonstrated in recent research, the process requires several iterations and can be time-consuming. By breaking down the source term function into series, the current work introduced a new decomposition approach to the Adomian decomposition method. As compared to the conventional Adomian decomposition approach, the newly devised method hastens the convergence of the solution. Numerical experiments were provided to show the superiority qualities.

Keywords

Infinite Series; Source Term; Convergence; Decomposition Methods

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References

J. Manafianheris, “Solving the integro-differential equations usingthe modified laplace adomian decomposition method,” Journal of Mathematical Extension, vol. 6, no. 1, pp. 1–15, 2012.

B. N. Saray, “An efficient algorithm for solving Volterra integro-differential equations based on alpert’s multi-wavelets Galerkin method,” Journal of Computational and Applied Mathematics, vol. 348, pp. 453–465, 2019, doi: 10.1016/j.cam.2018.09.016.

M. Olayiwola, A. Gbolagade, and F. Akinpelu, “Numerical solutions of generalized burger’shuxley equation by modified variational iteration method,” Journal of the Nigerian Association of Mathematical Physics, vol. 17, pp. 433–438, 2010.

M. Olayiwola, F. Akinpelu, and A. Gbolagade, “Modified variational iteration method for the solution of a class of differential equations,” American Journal of Computational and Applied Mathematics, vol. 2, no. 5, pp. 228–231, 2012, doi: 10.5923/j.ajcam.20120205.05.

A. I. Alaje, M. O. Olayiwola, K. A. Adedokun, J. A. Adedeji, and A. O. Oladapo, “Modified homotopy perturbation method and its application to analytical solitons of fractional-order korteweg–de vries equation,” Beni-Suef University Journal of Basic and Applied Sciences, vol. 11, no. 1, p. 139, 2022, doi: 10.1186/s43088-022-00317-w.

A. A.-E. Ibrahim, A. A. S. Zaghrout, K. R. Raslan, and K. K. Ali, “On the analytical and numerical study for nonlinear fredholm integro-differential equations,” Applied Mathematics & Information Sciences, vol. 14, no. 5, pp. 921–929, 2020, doi: 10.18576/amis/140520.

N. Sweilam, “Fourth order integro-differential equations using variational iteration method,” Computers & Mathematics with Applications, vol. 54, no. 7, pp. 1086–1091, 2007, variational Iteration Method for Nonlinear Problems.

M. Ogunniran, A. Alabi, Q. Amobi, and S. Emmanuel, “Fourth derivative block method for solving two-point singular boundary value problems and related stiff problems,” Turkish Journal of Science, vol. 6, no. 2, pp. 50 – 60, 2021.

A. Alaje, M. Olayiwola, M. Ogunniran, J. Adedeji, and K. Adedokun, “Approximate analytical methods for the solution of fractional order integro-differential equations,” Nigerian Journal of Mathematics and Applications, vol. 31, p. 175, 2021.

M. Olayiwola, A. Gbolagade, and A. Adesanya, “Solving variable coefficient fourth-order parabolic equation by modified initial guess variational iteration method,” Journal of the Nigerian Association of Mathematical Physics, vol. 16, pp. 205–210, 2010.

——, “An efficient algorithm for solving the telegraph equation,” Journal of the Nigerian Association of Mathematical Physics, vol. 16, pp. 199–2014, 2010.

M. Alqarni, R. Amin, K. Shah, S. Nazir, M. Awais, N. A. Alshehri, and E. E. Mahmoud, “Solution of third order linear and nonlinear boundary value problems of integro-differential equations using haar wavelet method,” Results in Physics, vol. 25, p.104176, 2021, doi: 10.1016/j.rinp.2021.104176.

J. Chen, M. He, and Y. Huang, “A fast multiscale galerkin method for solving second order linear fredholm integro-differential equation with Dirichlet boundary conditions,” Journal of Computational and Applied Mathematics, vol. 364, p. 112352, 2020, doi: 10.1016/j.cam.2019.112352.

N. Rohaninasab, K. Maleknejad, and R. Ezzati, “Numerical solution of high-order VolterraFredholm integro-differential equations by using legendre collocation method,” Applied Mathematics and Computation, vol. 328, pp. 171–188, 2018, doi: 10.1016/j.amc.2018.01.032.

S. M. Yassein, “Application of iterative method for solving higher order integro-differential equations,” Ibn AL-Haitham Journal For Pure and Applied Sciences, vol. 32, no. 2, pp. 51–61, 2019, doi: 10.30526/32.2.2139.

D. Rani and V. Mishra, “Solutions of volterra integral and integro-differential equations using modified laplace adomian decomposition method,” Journal of Applied Mathematics, Statistics and Informatics, vol. 15, no. 1, pp. 5–18, 2019, doi: 10.2478/jamsi-2019-0001.

A. K. Jimoh, “Integrated trapezoidal collocation method for solving third order integrodifferential equations,” International Journal of Scientific & Engineering Research, vol. 10, no. 7, pp. 1–14, 2019.

M. O. Olayiwola and K. Kareem, “A new decomposition method for integro-differential equations,” Cumhuriyet Science Journal, vol. 43, no. 2, pp. 283–288, 2022, doi: 10.17776/csj.986019.

M. Olayiwola, A. Gbolagade, and F. Akinpelu, “An efficient algorithm for solving the nonlinear pde,” International Journal of Scientific and Engineering Research, vol. 2, no. 10, pp. 1–10, 2011.

K. Kareem and M. Olayiwola, “Some results on fourth-order integro-differential equations. annals computer science series,” Anale. Seria Informatic˘a. Annals. Computer Science Series, vol. 18, no. 1, pp. 183–185, 2020.

R. Amin, I. Mahariq, K. Shah, M. Awais, and F. Elsayed, “Numerical solution of the second order linear and nonlinear integro-differential equations using haar wavelet method,” Arab Journal of Basic and Applied Sciences, vol. 28, no. 1, pp. 12–20, 2021.

DOI: https://doi.org/10.34312/jjom.v5i2.19029