Linear Multistep Methods for First-Order ODEs

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This Demonstration presents some linear multistep methods with certain parameters for solving first-order ordinary differential equations (ODEs). The name, structure and region of absolute stability of each method is shown.

Contributed by: Wusu Ashiribo Senapon and Akanbi Moses Adebowale (August 2017)
(Department of Mathematics, Lagos State University, Lagos, Nigeria)
Open content licensed under CC BY-NC-SA



The algorithm used in the methods presented in this Demonstration is based on the Newton backward difference interpolating polynomial. The problem is integrated over the interval , and is replaced by a polynomial obtained using Newton's backward difference interpolation scheme. The regions of absolute stability of the methods are found using the locus boundary method.

The control labels are described as follows:

"step number"—the step number of the method.

"initial range"—the value of in the interval .

"implicitness"—the value 0 is assigned to an explicit method, while the value 1 is assigned to an implicit method.


[1] M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Engineering Computation, 5th ed., New Delhi: New Age International, 2007.

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

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