InitialSeeding

InitialSeeding

is an option for NDSolve and other functions that specifies equations that specify initial seeding values for variables that may be used by iterative algorithms.

Details

  • For differential algebraic equations in NDSolve and other functions, InitialSeeding->{u[t0]==val} indicates that the numerical value val should be used to start finding consistent initial conditions.
  • For stationary nonlinear partial differential equations in NDSolve and other functions, InitialSeeding->{u[x1,]==fun[x1,]} indicates the numerical function fun of the independent variables x1, should be used to get a starting vector on the mesh.
  • Different initial seeding values may lead to different solutions. »

Examples

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Basic Examples  (1)

Specify an initial seeding of 0 for a boundary value problem:

Scope  (7)

Specify an initial seeding that depends on a spatial coordinate:

Use the solution of a linear boundary value problem as the initial seeding for a nonlinear boundary value problem:

Different settings for InitialSeeding can lead to different solutions of boundary value problems:

Specify a different value for the StartingGuess:

Specify a complex-valued initial seed:

Find a solution to a boundary value problem:

Find a different solution by specifying a different setting for InitialSeeding:

Give different initial seedings for the "Shooting" method for a nonlinear boundary value problem:

With the "Shooting" method, initial seeding can also be given inside of the solution interval:

Use InitialSeeding that is used to find consistent initial conditions for a system of differential algebraic equations:

Possible Issues  (2)

For certain DAE systems, a message about inconsistent initial condition may be issued if no initial seeding is specified:

Provide an initial condition seeding to get consistent initial conditions:

Different initial seeding values can lead to different results for DAE systems:

Specify a different starting guess:

Introduced in 2019
 (12.0)