Linear Multistep Methods Generator for First-Order ODEs

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This Demonstration describes several -step linear multistep methods for solving first-order ordinary differential equations. The name of the method, recursion relation, order, local truncation error and locus of the boundary of the region of absolute stability are shown for each case.

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A vertical line means that the stability interval is either empty or is the interval .

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Contributed by: Wusu Ashiribo Senapon (May 2018)
(Department of Mathematics, Lagos State University, Lagos, Nigeria)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The linear multistep methods (LMMs) described in this Demonstration are constructed using the maximal order approach. The name, recursion relation, order, local truncation error and locus of the boundary of the region of absolute stability for each method are presented. The locus boundary technique was used to obtain the locus of the boundary of the region of absolute stability of the methods.

Control labels:

"step number"—the step number of the LMM to be constructed.

"method"—name of the method used.

The present Demonstration is an update of Linear Multistep Methods for First-Order ODEs.

Reference

[1] J. D. Lambert, Computational Methods in Ordinary Differential Equations, New York: John Wiley and Sons, 1973.



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