AN INTEGRAL TRANSFORM TOGETHER WITH TAYLOR SERIES AND DECOMPOSITION METHOD FOR THE SOLUTION OF NONLINEAR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER

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Published: Feb 27, 2023
DOI: https://doi.org/10.22452/mjs.vol42no1.6
Keywords:
Aboodh Transform Adomian Decomposition Taylor Series Twelfth Thirteenth Order

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E. I. Akinola
Bowen University, PMB 284, Iwo, Osun State, NIGERIA.
https://orcid.org/0000-0003-0725-8437
Johnson Adekunle Owolabi
Bowen University, PMB 284, Iwo, Osun State, NIGERIA.
https://orcid.org/0000-0003-2084-799X
S. Alao
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000, Ogbomoso, Oyo State, NIGERIA.
O. S. Sangoniyi
Mathematics Department, Emmanuel Alayande College of Education, Oyo, Oyo State, NIGERIA.

Abstract

This work aims to determine the approximate solutions of nonlinear boundary value problems of higher order obtained through the Aboodh Transform Series Decomposition Method (ATSDM), a method designed to find the integral and the inverse transform of the problems, expand the exponential function, and simultaneously decompose the nonlinear terms. The results obtained demonstrate that ATSDM is an excellent and trusted approximate method that can be employed to obtain accurate results for any problem similar to the one presented in this work.

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How to Cite
Akinola, E. I. ., Owolabi, J. A., Alao, S. ., & Sunday Oloruntoyin Sangoniyi. (2023). AN INTEGRAL TRANSFORM TOGETHER WITH TAYLOR SERIES AND DECOMPOSITION METHOD FOR THE SOLUTION OF NONLINEAR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER. Malaysian Journal of Science, 42(1), 62–67. https://doi.org/10.22452/mjs.vol42no1.6
Issue
Vol 42 No 1 (2023): February
Section
Original Articles

Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

References

Abbaoui, K., & Cherruault, Y. (1994). Convergence of Adomian's method applied to differential equations. Computers & Mathematics with Applications, 28(5), 103-109.

Abdelbagy, A., Alshikh., Mohand, M., Abdelrahim Mahgoub.( 2016). Solving System of Ordinary Differential Equations by Aboodh Transform. World Applied Sciences Journal. 34(9):1144-1148.

Aboodh, K. S. (2013). The New Integral Transform'Aboodh Transform. Global Journal of Pure and Applied Mathematics, 9(1), 35-43.

Aboodh, K. S. (2014). Application of new transform “Aboodh Transform” to partial differential equations. Global Journal of Pure and Applied Mathematics, 10(2), 249-254.

Adeyefa, E. O., & Kuboye, J. O. (2020). Derivation of New Numerical Model Capable of Solving Second and Third Order Ordinary Differential Equations Directly. IAENG International Journal of Applied Mathematics, 50(2), 1-9.

Adomian, G. (1988). A review of the decomposition method in applied mathematics. Journal of mathematical analysis and applications, 135(2), 501-544.

Agarwal, R. P. (1986). Boundary value problems from higher order differential equations. World Scientific.

Akinola, E. I., Akinpelu, F. O., Areo, A. O., Akanni, J. O., & Oladejo, J. K. (2017). The Mathematical Formulation of Laplace Series Decomposition Method for Solving Nonlinear Higher-Order Boundary Value Problems in Finite Domain.

Akinola, E. I., Olopade, I. A., Akinpelu, F. O., Areo, A. O., & Oyewumi, A. A. (2016). Sumudu Transform Series Decomposition Method for Solving Nonlinear Volterra Integro-Differential Equations.

Amer, Y. A., Mahdy, A. M. S., Shwayaa, T. T., & Youssef, E. S. M. (2018). Laplace transform method for solving nonlinear biochemical reaction model and nonlinear Emden-Fowler system. Journal of Engineering and Applied Sciences, 13(17), 7388-7394.

Chandrasekhar, S. (1961). Hydromagnetic and Hydrodynamic Stability, Clarendon.

El-Gamel, M. (2015). Chebychev polynomial solutions of twelfth-order boundary-value problems. Journal of Advances in Mathematics and Computer Science, 13-23.

Farooq, M. A., Razia, S., & Mushtaq, A. (2020). Numerical comparison of constant and variable fluid properties for MHD flow over a nonlinearly stretching sheet.

Gbadamosi, B., Adebimpe, O., Akinola, E. I., & Olopade, I. A. (2012). Solving Riccati equation using Adomian decomposition method.

Gepreel, K. A., Higazy, M., & Mahdy, A. M. S. (2020). Optimal control, signal flow graph, and system electronic circuit realization for nonlinear Anopheles mosquito model. International Journal of Modern Physics C, 31(09), 2050130.

Hassan, I. A. H., Othman, M. I., & Mahdy, A. M. S. (2009). Variational iteration method for solving twelve order boundary value problems. International Journal of Mathematical Analysis, 3(13-16), 719-730.

Hymavathi, T., & Kumar, P. V. (2014). Numerical Solution of Twelfth Order Boundary Value Problems Using Homotopy Analysis Method. Journal of Engineering, Computers & Applied Sciences (JEC & AS) Volume, 3.

Mahdy, A. M. S., & Higazy, M. (2019). Numerical different methods for solving the nonlinear biochemical reaction model. International Journal of Applied and Computational Mathematics, 5(6), 1-17.

Mahdy, A. M. S., & Youssef, E. S. M. (2021). Numerical solution technique for solving isoperimetric variational problems. International Journal of Modern Physics C, 32(01), 2150002.

Mahdy, A. M. S., Mohamed, M. S., Lotfy, K., Alhazmi, M., El-Bary, A. A., & Raddadi, M. H. (2021). Numerical solution and dynamical behaviors for solving fractional nonlinear Rubella ailment disease model. Results in Physics, 24, 104091.

Mahdy, A. M., Amer, Y. A. E., Mohamed, M. S., & Sobhy, E. (2020). General fractional financial models of awareness with Caputo–Fabrizio derivative. Advances in Mechanical Engineering, 12(11), 1687814020975525.

Mahgoub, M. M. A., & Sedeeg, A. K. H. (2017). An efficient method for solving linear and nonlinear system of partial differential equations. Journal of Advances in Mathematics and Computer Science, 1-10.

Mohyud-din, S.T. (2009). Exp-function method for solving higher order boundary value problems. Bulletin of the Institute of Mathematics, Academia Sinica, 4(2):219-234

Noor, M. A., & Mohyud-Din, S. T. (2008). Solution of twelfth-order boundary value problems by variational iteration technique. Journal of Applied Mathematics and Computing, 28(1), 123-131.

Oderinu, R. A. (2014). On the numerical solution of tenth and twelfth order boundary value problems using weighted residual method (WRM). Gen. Math. Notes, 24(1), 17-24.

Opanuga, A. A., Okagbue, H. I., & Agboola, O. O. (2017). Application of Semi-Analytical Technique for Solving Thirteenth Order Boundary Value Problem.

Opanuga, A. A., Okagbue, H. I., Edeki, S. O., & Agboola, O. O. (2015). Differential transform technique for higher order boundary value problems. Modern Applied Science, 9(13), 224-230.

Othman, M. I., Mahdy, A. M. S., & Farouk, R. M. (2010). Numerical solution of 12th order boundary value problems by using homotopy perturbation method. Journal of Mathematics and Computer Science, 1(1), 14-27.

Owolabi, J. A., Ige, O. E., & Akinola, E. I. (2019). Application of Kamal Decomposition Transform Method in Solving Two-Dimensional Unsteady Flow. International Journal of Difference Equations (IJDE), 14(2), 207-214.

Siddiqi, S. S., Akram, G., & Zulfiqar, I. (2009). Solution of twelfth order boundary value problems using variational iteration technique. Eur. J. Sci. Res, 33(1), 96-114.

Wazwaz, A. M. (2000). Approximate solutions to boundary value problems of higher order by the modified decomposition method. Computers & Mathematics with Applications, 40(6-7), 679-691.

Wazwaz, A. M. (2000a). The modified Adomian decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth-order. International Journal of Nonlinear Sciences and Numerical Simulation, 1(1), 17-24.

Yalçinbaş, S. (2002). Taylor polynomial solutions of nonlinear Volterra–Fredholm integral equations. Applied Mathematics and Computation, 127(2-3), 195-206.