An algorithm for second order initial and boundary value problems with an automatic error estimate based on a third derivative method

Authors:
Samuel N. Jator;Jiang Li
Affiliations:
Department of Mathematics and Statistics, Austin Peay State University, Clarksville, USA 37044;Department of Computer Science and Information Technology, Austin Peay State University, Clarksville, USA 37044
Venue:
Numerical Algorithms
Year:
2012

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Abstract

A third derivative method (TDM) with continuous coefficients is derived and used to obtain a main and additional methods, which are simultaneously applied to provide all approximations on the entire interval for initial and boundary value problems of the form y驴驴驴=驴f(x, y, y驴). The convergence analysis of the method is discussed. An algorithm involving the TDMs is developed and equipped with an automatic error estimate based on the double mesh principle. Numerical experiments are performed to show efficiency and accuracy advantages.