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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
Chollom JP. Some properties of the block linear-multi-step methods. Afr J online 2007; 2(3).
Chollom JP, Jackiewicz International Journal of Numerical Mathematics (ijnmonline.org/doc/58-75).
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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