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Four Steps Continuous Method for the Solution of <i>y″</i>= <i>f</i> (<i>x, y, y′</i>)
Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
Department of Mathematics and Statistics, Cross River State University of Technology, Calabar, Nigeria
- 1 Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
- 2 Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria
- 3 Department of Mathematics and Statistics, Cross River State University of Technology, Calabar, Nigeria
American Journal of Computational Mathematics·Volume 03 (2013)·Pages 169–174·Published 17 June 2013·DOI10.4236/ajcm.2013.32025
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Abstract
This paper proposes a continuous block method for the solution of second order ordinary differential equation. Collocation and interpolation of the power series approximate solution are adopted to derive a continuous implicit linear multistep method. Continuous block method is used to derive the independent solution which is evaluated at selected grid points to generate the discrete block method. The order, consistency, zero stability and stability region are investigated. The new method was found to compare favourably with the existing methods in term of accuracy.
KeywordsPredictorCorrectorCollocationInterpolationPower Series ApproximantContinuous Block Method
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