Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals

• Published in: SpringerPlus Vol. 3; no. 1; pp. 160 - 7
• Main Authors: Vazquez-Leal, Hector, Benhammouda, Brahim, Filobello-Nino, Uriel Antonio, Sarmiento-Reyes, Arturo, Jimenez-Fernandez, Victor Manuel, Marin-Hernandez, Antonio, Herrera-May, Agustin Leobardo, Diaz-Sanchez, Alejandro, Huerta-Chua, Jesus
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 25.03.2014; Springer Nature B.V; BioMed Central Ltd
• Subjects: Applied Mathematics; Boundary conditions; Differential equations; Humanities and Social Sciences; multidisciplinary; Science; Science (multidisciplinary); Boundary valued problems; Mixed boundary conditions; Taylor series method; Shooting technique; Dirichlet conditions
• ISSN: 2193-1801; 2193-1801
• DOI: 10.1186/2193-1801-3-160

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. AMS Subject Classification 34L30