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A Direct Numerical Integration Method for Second‐Order Ordinary Differential Equations
Author(s) -
Gupta R. G.
Publication year - 1975
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19750551203
Subject(s) - ordinary differential equation , truncation error , runge–kutta methods , numerical integration , mathematics , numerical methods for ordinary differential equations , order (exchange) , truncation (statistics) , function (biology) , direct methods , value (mathematics) , butcher , direct integration of a beam , numerical analysis , differential equation , mathematical analysis , physics , collocation method , statistics , law , finance , nuclear magnetic resonance , evolutionary biology , economics , biology , thermodynamics , political science
This paper describes a new direct method for the numerical integration of the initial value problem\documentclass{article}\pagestyle{empty}\begin{document}$$ y''(x)\;f(x,\;y(x),\;y'(x));\;y(x_0)\; = y'_0 $$\end{document} . The method has a local truncation error O(h 6 ) in y(x) and O(h 5 ) in y'(x). For n integration steps, the present method requires 5 n function evaluations while the method of Runge‐Kutta‐Butcher needs 6 n for the same order of accuracy. Theoretical and computational comparisons of the present method with the existing methods are discussed.