lsoda (Livermore Solver for Ordinary Differential Equations)

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Functions list:

Mostra spoiler

lsoda(ics, xmin, xmax, steps, ode) solves the initial value problem for stiff or nonstiff systems (uses Adams/BDF methods).

Arguments:

• ics is either a vector of n real initial values, where n is the number of unknowns (or a single scalar initial value, in the case of a single ODE).
  
• xmin and xmax are real, scalar endpoints of the interval over which the solution to the ODE(s) is evaluated. Initial values in init are the values of the ODE function(s) evaluated at x1.
  
• steps is the integer number of discretization intervals used to interpolate the solution function. The number of solution points is the number of intervals + 1.
  
• ode is a vector function of the form D(x,y) specifying the right-hand side of the system

Options:

- AbsTol - absolute tolerance parameter, default value 10⁻⁷.
- RelTol - relative tolerance parameter, default value 10⁻⁴.




Links:

1. Solving Stiff ODEs.
2. Serial Fortran Solvers for ODE Initial Value Problems.

lsoda.integrate.sm (10,55 KiB) scaricato 1908 volta(e).
lsoda.kinetic1.sm (7,74 KiB) scaricato 1828 volta(e).
lsoda.kinetic2.sm (10,74 KiB) scaricato 1838 volta(e).
lsoda.kinetic3.sm (10,42 KiB) scaricato 1798 volta(e).
lsoda.test1.sm (11,63 KiB) scaricato 1820 volta(e).
lsoda.test2.sm (11,3 KiB) scaricato 1817 volta(e).
lsoda.Arenstorf Orbit.sm (15,45 KiB) scaricato 1982 volta(e).
lsoda.Amplitude detector.sm (20,15 KiB) scaricato 1869 volta(e).

lsoda.integrate.pdf (87 KiB) scaricato 1045 volta(e).
lsoda.kinetic1.pdf (74,4 KiB) scaricato 1095 volta(e).
lsoda.kinetic2.pdf (87,83 KiB) scaricato 963 volta(e).
lsoda.kinetic3.pdf (82,48 KiB) scaricato 923 volta(e).
lsoda.test1.pdf (87,33 KiB) scaricato 971 volta(e).
lsoda.test2.pdf (90,52 KiB) scaricato 949 volta(e).
lsoda.Arenstorf Orbit.pdf (93,42 KiB) scaricato 1076 volta(e).
lsoda.Amplitude detector.pdf (148,2 KiB) scaricato 1045 volta(e).

See also:

● [topic=726]Mathcad Toolbox[/topic]
● [topic=1918]DotNumerics[/topic]
● [topic=13809]SADEL[/topic]
● [topic=1970]Matlab C++ Math Library[/topic]
● [topic=17063]OSLO[/topic]
● [topic=1997]GNU Scientific Library (GSL)[/topic]

Hello Viacheslav,

I attach here the two different file, lsodaMAP3 have the problem solved, lsodaMAP2 show the error.


SMath version 0.99.7610.506
lsoda version 0.1.7175.9902

File non trovato. File non trovato. File non trovato.

Playing a little bit in the lsodaMAP2 I was able to make it show the chart with the "problem".


Let me know if you need anything else!

All the best

Francesco

The problem is in the X-Y Plot plugin. It cannot display the input data because it is outside the normal bounds. Also in the document somehow the min and max values of the axis are the same, which also results in an error. It will take a time to fix this. I haven't tested the plugin on bad data much.

Plugin updated.

Changes:

- added support for ODE systems in mathematical form;
- refactored.

Plugin updated.

Changes:

- solution restructured;
- converting the task for the ODE solver to the numerical form is now performed through the Mathcad Toolbox plugin (to avoid code duplication), so it must be installed;
- refactored.

Solvers that support mathematical notation now reuse code from the Mathcad Toolbox plugin. Now there is no need to recompile every such plugin. As far as I understand, the algorithm used in this solver is the same as used in Odesolve: Adams/BDF. This can be seen from the comments in the source code. If I can port this code to c#, then we will have the same solver as in Mathcad. I want to include it as a default solver in Mathcad Toolbox plugin.