Block Methods based on Newton Interpolations for Solving Special Second Order Ordinary Differential Equations Directly
This study focused mainly on the derivation of the 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results were presented to illustrate the effectiveness of the methods in terms of total number of steps taken, maximum error and execution time. The results suggested a significant improvement in efficiency of the r-point block method. AMS Subject Classification: 65L05.
Copyright: © 2008 Yap Lee Ken, Fudziah Ismail, Mohamed Suleiman and Suriah Md. Amin. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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- Initial value problems
- special second order ordinary differential equations
- block method