Research Article
BibTex RIS Cite

A New Decomposition Method for Integro-Differential Equations

Year 2022, Volume: 43 Issue: 2, 283 - 288, 29.06.2022

Morufu Oyedunsi Olayiwola , Kabiru Kareem

https://doi.org/10.17776/csj.986019
Cited By: 2

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.
  • [11] Hamoud A.A., Ghadle K.P., Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, Journal of Mathematical Modeling, 6(1) (2018b) 91-104.
  • [12] Ibrahim, H., Ayoo P. V., Approximation of systems of Volterra integro-differential equations using the new iterative method, International Journal of Science and Research, 4(5) (2015) 332-336.
  • [13] Kumar K., Pandey R.K., Sharma, S., Comparative study of three numerical schemes for fractional integro-differential equations, Journal of Computational and Applied Mathematics, 315(2017) 287-302.
  • [14] Ma X., Huang, C., Spectral collocation method for linear fractional integro-differential equations, Applied Mathematical Modelling, 38 (2014) 1434-1448.
  • [15] Nemati S., Sedaghat S., Mohammadi, I., A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels, Journal of Computational and Applied Mathematics, 308 (2016) 231-242.
  • [16] Ordokhani Y., Dehestani H., Numerical solution of linear Fredholm-Volterra integro-differential equations of fractional order, World Journal of Modelling and Simulation, 12(3) (2016) 204-216.
  • [17] Turmetov B., Abdullaev J., Analytic solutions of fractional integro-differential equations of Volterra type, IOP Conference Series, Journal of Physics: Conference Series, 890 (2017) 012113.
  • [18] Wang Y., Zhu L., SCW method for solving the fractional integro-differential equations with a weakly singular kernel, Applied Mathematics and Computation, 275 (2016) 72-80.
  • [19] Yi M., Wang L., Huang, J., Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel, Applied Mathematical Modelling, 40 (2016) 3422-3437.
  • [20]Mahdy A.M.S., Shwayyea R.T., Numerical solution of fractional integro-differential equations by least squares method and shifted Laguerre polynomials pseudo-spectral method, International Journal of Scientific & Engineering Research, 7(4) (2016) 1589-1596.
  • [21] Oyedepo T., Taiwo O.A., Abubakar J.U., Ogunwobi Z.O., Numerical studies for solving fractional integro-differential equations by using least squares method and Bernstein polynomials, Fluid Mechanics: Open Access, 3(3) (2016) 1000142.
  • [22] Syam M.I., Analytical solution of the fractional Fredholm integrodifferential equation using the fractional residual power series method, Complexity 2017, 4573589.
  • [23]Gülsu M., Öztürk Y., Anapalı A., Numerical approach for solving fractional Fredholm integro-differential equation, International Journal of Computer Mathematics, 90(7) (2013) 1413-1434.
  • [24]Kobayashi R., Konuma M., Kumano, S., Fortran program for a numerical solution of the nonsinglet Altarelli-Parisi equation, Computer Physics Communications, 86 (1995) 264-278.
  • [25]Pandey P.K., Numerical Solution of Linear Fredholm Integro-Differential Equations by Non-standard Finite Difference Method, Applications and Applied Mathematics:An International Journal, 10(2) (2015) 1019-1026.
  • [26]Yüzbaşı Ş., Laguerre approach for solving pantograph-type Volterra integro-differential equations, Applied Mathematics and Computation, 232 (2014) 1183-1199.
  • [27] Karim M.F., Mohamad M., Rusiman M.S., Che-HIM N., Roslan, R., Khalid, K., ADM for solving linear second-order fredholm integro- differential equations. IOP Conf. Series: Journal of Physics, 995 (2018) Doi: 10.1088/1742-6596/995/1/012009.
  • [28]Wazwaz A.M., First course in integral equations, 2nd. Ed. Singapore: World Scientific Publishing Co. Pte. Ltd., (2015) 596224.
  • [29]Olayiwola M. O., Ogunniran M. O., Variational iteration method for solving higher-order integro-differential equations, Nigerian Journal of Mathematics and Application, B29 (2019) 18-23.
  • [30] Olayiwola M. O., Adedokun K. A., Gbolagade A. W., Solving linear and non linear integro-differential equations using modified Adomian decomposition method, IslamicUniversity Multidisciplinary Journal 6(3) (2019) 202-209.

Year 2022, Volume: 43 Issue: 2, 283 - 288, 29.06.2022

Morufu Oyedunsi Olayiwola , Kabiru Kareem

https://doi.org/10.17776/csj.986019
Cited By: 2

Abstract

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.
  • [11] Hamoud A.A., Ghadle K.P., Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, Journal of Mathematical Modeling, 6(1) (2018b) 91-104.
  • [12] Ibrahim, H., Ayoo P. V., Approximation of systems of Volterra integro-differential equations using the new iterative method, International Journal of Science and Research, 4(5) (2015) 332-336.
  • [13] Kumar K., Pandey R.K., Sharma, S., Comparative study of three numerical schemes for fractional integro-differential equations, Journal of Computational and Applied Mathematics, 315(2017) 287-302.
  • [14] Ma X., Huang, C., Spectral collocation method for linear fractional integro-differential equations, Applied Mathematical Modelling, 38 (2014) 1434-1448.
  • [15] Nemati S., Sedaghat S., Mohammadi, I., A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels, Journal of Computational and Applied Mathematics, 308 (2016) 231-242.
  • [16] Ordokhani Y., Dehestani H., Numerical solution of linear Fredholm-Volterra integro-differential equations of fractional order, World Journal of Modelling and Simulation, 12(3) (2016) 204-216.
  • [17] Turmetov B., Abdullaev J., Analytic solutions of fractional integro-differential equations of Volterra type, IOP Conference Series, Journal of Physics: Conference Series, 890 (2017) 012113.
  • [18] Wang Y., Zhu L., SCW method for solving the fractional integro-differential equations with a weakly singular kernel, Applied Mathematics and Computation, 275 (2016) 72-80.
  • [19] Yi M., Wang L., Huang, J., Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel, Applied Mathematical Modelling, 40 (2016) 3422-3437.
  • [20]Mahdy A.M.S., Shwayyea R.T., Numerical solution of fractional integro-differential equations by least squares method and shifted Laguerre polynomials pseudo-spectral method, International Journal of Scientific & Engineering Research, 7(4) (2016) 1589-1596.
  • [21] Oyedepo T., Taiwo O.A., Abubakar J.U., Ogunwobi Z.O., Numerical studies for solving fractional integro-differential equations by using least squares method and Bernstein polynomials, Fluid Mechanics: Open Access, 3(3) (2016) 1000142.
  • [22] Syam M.I., Analytical solution of the fractional Fredholm integrodifferential equation using the fractional residual power series method, Complexity 2017, 4573589.
  • [23]Gülsu M., Öztürk Y., Anapalı A., Numerical approach for solving fractional Fredholm integro-differential equation, International Journal of Computer Mathematics, 90(7) (2013) 1413-1434.
  • [24]Kobayashi R., Konuma M., Kumano, S., Fortran program for a numerical solution of the nonsinglet Altarelli-Parisi equation, Computer Physics Communications, 86 (1995) 264-278.
  • [25]Pandey P.K., Numerical Solution of Linear Fredholm Integro-Differential Equations by Non-standard Finite Difference Method, Applications and Applied Mathematics:An International Journal, 10(2) (2015) 1019-1026.
  • [26]Yüzbaşı Ş., Laguerre approach for solving pantograph-type Volterra integro-differential equations, Applied Mathematics and Computation, 232 (2014) 1183-1199.
  • [27] Karim M.F., Mohamad M., Rusiman M.S., Che-HIM N., Roslan, R., Khalid, K., ADM for solving linear second-order fredholm integro- differential equations. IOP Conf. Series: Journal of Physics, 995 (2018) Doi: 10.1088/1742-6596/995/1/012009.
  • [28]Wazwaz A.M., First course in integral equations, 2nd. Ed. Singapore: World Scientific Publishing Co. Pte. Ltd., (2015) 596224.
  • [29]Olayiwola M. O., Ogunniran M. O., Variational iteration method for solving higher-order integro-differential equations, Nigerian Journal of Mathematics and Application, B29 (2019) 18-23.
  • [30] Olayiwola M. O., Adedokun K. A., Gbolagade A. W., Solving linear and non linear integro-differential equations using modified Adomian decomposition method, IslamicUniversity Multidisciplinary Journal 6(3) (2019) 202-209.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Morufu Oyedunsi Olayiwola 0000-0001-6101-1203

Kabiru Kareem 0000-0002-7457-5945

Publication Date June 29, 2022
Submission Date August 22, 2021
Acceptance Date April 17, 2022
Published in Issue Year 2022Volume: 43 Issue: 2

Cite

APA Olayiwola, M. O., & Kareem, K. (2022). A New Decomposition Method for Integro-Differential Equations. Cumhuriyet Science Journal, 43(2), 283-288. https://doi.org/10.17776/csj.986019

Cited By

Solving linear systems of fractional integro-differential equations by Haar and Legendre wavelets techniques
Partial Differential Equations in Applied Mathematics
https://doi.org/10.1016/j.padiff.2024.100683
COLLOCATION METHOD APPLIED TO NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS
Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi
https://doi.org/10.17780/ksujes.1346489
 Download Cover Image