11428

Linear Multistep Methods for First-Order ODEs

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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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.
References
[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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+