Where Can Adams-Bashforth-Moulton Method be Applied in Real-World Sciences?

[iwan89]

What are the applications of Adams-Bashforth-Moulton Method for O.D.E.'s in the real world? How we could utilize this method in other branches of science?

 

[SteamKing]

Is this HW by any chance?

 

[iwan89]

No.. i just want to know the application. Adams bashforth somehow may have applications in other branch of science

 

[AlephZero]

Many of the methods you learn in a first course on numerical solutions of ODEs and PDEs are taught more for their educational value than for being the current state of the art. Adams and Bashforth first published their method about 130 years ago, long before digital computers existed!

The general idea of multistep methods http://en.wikipedia.org/wiki/Linear_multistep_method is still used, but not necessarily the specifics of the ABM method.

 

[Chestermiller]

Adams Bashforth integration is an option offered in most packaged ODE solvers that specialize in stiff ODEs. The method solves each integration step implicitly, but it solves the implicit equations by successive substitution, rather than by Newton Raphson. Adams Bashforth is less computationally intense that Newton Raphson, but often will require many more iterations at each time step if the equations are very stiff and non-linear. So from the standpoint of computation time, Adams Bashforth may require much more computation time. Still, the nice feature of Adams Bashforth is an easily implemented automatic error control, which is built into the ODE packages.

Chet

 

[iwan89]

Thank you! I am trying to find the real application and use it to the program that i just created. I hope you guys could show me good example of the application of Adam Bashforth in other fields (Such as Engineering, Chemistry, Medical).