Reformulation of Adams-Moulton Block Methods as a Sub-Class of Two Step Runge-Kutta Method
DOI:
https://doi.org/10.6000/1927-5129.2014.10.03Keywords:
Reformulation, Adams-Moulton, block method, two-step, Runge-Kutta and collocation.Abstract
Adams-Moulton methods for k = 2 and k = 3 were constructed together with their continuous forms using multi-step collocation methods. The continuous forms were then evaluated at various grid points to produce the block Adams-Moulton methods.
The block methods were then reformulated as a sub-class of two step Runge-Kutta methods (TSRK). Both the Adams and the reformulated methods were applied to solve initial value problems and the reformulated methods proved superior in terms of stability.
References
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Onumanyi P, Awoyemi DO, Jatur NS, Sirisena UW. New Linear multi-step methods with continuous coefficients for first order IVPs. J Math Soc Nigeria 1994; 13.
Jackiewicz Z, Tracogna. A general class of two-step Runge – Kutta methods for ordinary differential Equations. SIAM J Numerical Anal Arch 1995; 32(5).
Lambert JD. Numerical methods for ordinary differential systems. John Wiley and sons, New York.
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