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
Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.
Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035, Abu Dhabi, United Arab Emirates.
Springerplus. 2014 Mar 25;3:160. doi: 10.1186/2193-1801-3-160. eCollection 2014.
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.
34L30.
在本文中，我们提出应用一种改进的泰勒级数方法（MTSM）来逼近有限区间上描述的非线性问题。利用射击常数和问题的额外导数规避了具有混合边界条件的泰勒级数方法的问题。为了展示该提议的优势，求解了三种不同类型的问题：具有双曲正弦非线性的三阶三点边值问题（BVP）、具有指数非线性的二阶非线性微分方程的两点BVP以及具有根式非线性的三阶非线性微分方程的两点BVP。结果表明，MTSM方法能够为非线性方程生成易于计算且高度精确的近似解。
34L30。
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