lsoda (Livermore Solver for Ordinary Differential Equations)

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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 KiB) downloaded 102 time(s).
lsoda.kinetic1.sm (7 KiB) downloaded 70 time(s).
lsoda.kinetic2.sm (10 KiB) downloaded 60 time(s).
lsoda.kinetic3.sm (10 KiB) downloaded 57 time(s).
lsoda.test1.sm (11 KiB) downloaded 65 time(s).
lsoda.test2.sm (11 KiB) downloaded 54 time(s).
lsoda.Arenstorf Orbit.sm (15 KiB) downloaded 87 time(s).
lsoda.Amplitude detector.sm (20 KiB) downloaded 55 time(s).

lsoda.integrate.pdf (87 KiB) downloaded 102 time(s).
lsoda.kinetic1.pdf (74 KiB) downloaded 78 time(s).
lsoda.kinetic2.pdf (87 KiB) downloaded 65 time(s).
lsoda.kinetic3.pdf (82 KiB) downloaded 68 time(s).
lsoda.test1.pdf (87 KiB) downloaded 84 time(s).
lsoda.test2.pdf (90 KiB) downloaded 64 time(s).
lsoda.Arenstorf Orbit.pdf (93 KiB) downloaded 79 time(s).
lsoda.Amplitude detector.pdf (148 KiB) downloaded 65 time(s).

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 not found. File not found. File not found.

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.