lsoda (Livermore Solver for Ordinary Differential Equations)

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Functions list:

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 (11kb) downloaded 52 time(s).
lsoda.kinetic1.sm (8kb) downloaded 39 time(s).
lsoda.kinetic2.sm (11kb) downloaded 32 time(s).
lsoda.kinetic3.sm (11kb) downloaded 31 time(s).
lsoda.test1.sm (12kb) downloaded 33 time(s).
lsoda.test2.sm (12kb) downloaded 31 time(s).
lsoda.Arenstorf Orbit.sm (16kb) downloaded 47 time(s).
lsoda.Amplitude detector.sm (21kb) downloaded 33 time(s).

lsoda.integrate.pdf (88kb) downloaded 58 time(s).
lsoda.kinetic1.pdf (75kb) downloaded 42 time(s).
lsoda.kinetic2.pdf (88kb) downloaded 39 time(s).
lsoda.kinetic3.pdf (83kb) downloaded 40 time(s).
lsoda.test1.pdf (88kb) downloaded 53 time(s).
lsoda.test2.pdf (91kb) downloaded 36 time(s).
lsoda.Arenstorf Orbit.pdf (94kb) downloaded 48 time(s).
lsoda.Amplitude detector.pdf (149kb) downloaded 38 time(s).

See also:

● Mathcad Toolbox
● DotNumerics
● SADEL
● Matlab C++ Math Library
● OSLO
● GNU Scientific Library (GSL)

Edited by user 23 December 2021 20:25:02(UTC)  | Reason: Not specified

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:

- 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.