On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method
This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through diff...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2021-05-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/15604 |
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| author | Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira |
| author_facet | Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira |
| author_sort | Gbeminiyi Musibau Sobamowo |
| collection | DOAJ |
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This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through different illustrative numerical examples. The method is shown to be conceptually and computationally simple and straightforward without any ambiguity. Also, the method as applied in this study shows that it does not require the development of any other iterative scheme that could be used to find the solution to the nonlinear equations. Additionally, the method does not require finding symbolic or numerical derivatives of any given function. With the use of the Adomian decomposition method, there is no search for an auxiliary parameter for adjusting and controlling the rate and region of convergence of the solution. The method does not require finding the correct fixed point and it is free from the problem of choosing an appropriate initial approximation. Therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science and engineering.
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| format | Article |
| id | doaj-art-5a8897f7bdf048539ca0bd380625a198 |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2021-05-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-5a8897f7bdf048539ca0bd380625a1982025-02-02T19:57:03ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752021-05-017310.18540/jcecvl7iss3pp15604-01eOn the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition MethodGbeminiyi Musibau Sobamowo0Antonio Marcos de Oliveira Siqueira1University of Lagos, NigeriaFederal University of Viçosa, Brazil This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through different illustrative numerical examples. The method is shown to be conceptually and computationally simple and straightforward without any ambiguity. Also, the method as applied in this study shows that it does not require the development of any other iterative scheme that could be used to find the solution to the nonlinear equations. Additionally, the method does not require finding symbolic or numerical derivatives of any given function. With the use of the Adomian decomposition method, there is no search for an auxiliary parameter for adjusting and controlling the rate and region of convergence of the solution. The method does not require finding the correct fixed point and it is free from the problem of choosing an appropriate initial approximation. Therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science and engineering. https://periodicos.ufv.br/jcec/article/view/15604Nonlinear algebraic equations, Nonlinear transcendental equations; Approximate analytical solutions; Root-finding; Adomian decomposition method. |
| spellingShingle | Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method The Journal of Engineering and Exact Sciences Nonlinear algebraic equations, Nonlinear transcendental equations; Approximate analytical solutions; Root-finding; Adomian decomposition method. |
| title | On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method |
| title_full | On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method |
| title_fullStr | On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method |
| title_full_unstemmed | On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method |
| title_short | On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method |
| title_sort | on the solutions of nonlinear algebraic and transcendental equations using adomian decomposition method |
| topic | Nonlinear algebraic equations, Nonlinear transcendental equations; Approximate analytical solutions; Root-finding; Adomian decomposition method. |
| url | https://periodicos.ufv.br/jcec/article/view/15604 |
| work_keys_str_mv | AT gbeminiyimusibausobamowo onthesolutionsofnonlinearalgebraicandtranscendentalequationsusingadomiandecompositionmethod AT antoniomarcosdeoliveirasiqueira onthesolutionsofnonlinearalgebraicandtranscendentalequationsusingadomiandecompositionmethod |