Extension of Laplace transform–homotopy perturbation method to solve nonlinear differential equations with variable coefficients defined with Robin boundary conditions
| Autor: | J. Huerta-Chua, Hector Vazquez-Leal, Brahim Benhammouda, Arturo Sarmiento-Reyes, M. A. Sandoval-Hernandez, Victor Manuel Jimenez-Fernandez, Uriel Filobello-Nino, Luis J. Morales-Mendoza, A. Perez-Sesma, S. F. Hernandez-Machuca, J. M. Mendez-Perez, Mario Gonzalez-Lee, Yasir Khan |
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| Rok vydání: | 2015 |
| Předmět: |
Laplace transform
Mathematical analysis Inverse Laplace transform 010103 numerical & computational mathematics 01 natural sciences Robin boundary condition Poincaré–Lindstedt method 010305 fluids & plasmas Nonlinear system symbols.namesake Artificial Intelligence Laplace transform applied to differential equations 0103 physical sciences symbols Two-sided Laplace transform 0101 mathematics Software Homotopy analysis method Mathematics |
| Zdroj: | Neural Computing and Applications. 28:585-595 |
| ISSN: | 1433-3058 0941-0643 |
| DOI: | 10.1007/s00521-015-2080-z |
| Popis: | This article proposes the application of Laplace transform---homotopy perturbation method with variable coefficients, in order to find analytical approximate solutions for nonlinear differential equations with variable coefficients. As case study, we present the oxygen diffusion problem in a spherical cell including nonlinear Michaelis---Menten uptake kinetics. It is noteworthy that this important problem introduces the Robin boundary conditions as an additional difficulty. In fact, after comparing figures between approximate and exact solutions, we will see that the proposed solutions are highly accurate. What is more, we will see that the square residual error of our solutions is 1.808511632 × 10ź7 and 2.560574954 × 10ź10 which confirms the accuracy of the proposed method, taking into account that we will just keep the first-order approximation. |
| Databáze: | OpenAIRE |
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