Extension of Laplace transform–homotopy perturbation method to solve nonlinear differential equations with variable coefficients defined with Robin boundary conditions

详细信息    查看全文

• 作者：U. Filobello-Nino ; H. Vazquez-Leal ; Yasir Khan&#8230
• 关键词：Homotopy perturbation method ; Nonlinear differential equation ; Approximate solutions ; Laplace transform ; Laplace transform–homotopy perturbation method ; Oxygen cell ; Diffusion
• 刊名：Neural Computing and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：28
• 期：3
• 页码：585-595
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence (incl. Robotics); Data Mining and Knowledge Discovery; Probability and Statistics in Computer Science; Computational Science and Engineering; Image Processing and Computer Visi
• 出版者：Springer London
• ISSN：1433-3058
• 卷排序：28

文摘

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 × 10−7 and 2.560574954 × 10−10 which confirms the accuracy of the proposed method, taking into account that we will just keep the first-order approximation.