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InitialSeeding
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InitialSeeding

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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

open allclose all

Basic Examples  (1)Summary of the most common use cases

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-hfj486
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

Specify an initial seeding that depends on a spatial coordinate:

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-e6c86g
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-g23zfi
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-s0damc
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-v601e
Out[1]=1

Specify a different value for the StartingGuess:

In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-n6su0o
Out[2]=2

Specify a complex-valued initial seed:

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-vhheii
Out[1]=1

Find a solution to a boundary value problem:

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-4ndi86
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-88uqkc
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0n4oikqt8mi-3c35bt
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0n4oikqt8mi-da7nhp
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-8burp
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-cv0m5l
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0n4oikqt8mi-mfqp9t
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-p6susd
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-0bexxw
Out[2]=2

Possible Issues  (2)Common pitfalls and unexpected behavior

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-i63x6k
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-lu52t9
Out[2]=2

Provide an initial condition seeding to get consistent initial conditions:

In[3]:=3
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https://wolfram.com/xid/0n4oikqt8mi-pwxtkv
In[4]:=4
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https://wolfram.com/xid/0n4oikqt8mi-i5r48x
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0n4oikqt8mi-kr5hi1
In[2]:=2
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https://wolfram.com/xid/0n4oikqt8mi-gaomg2
Out[2]=2

Specify a different starting guess:

In[3]:=3
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https://wolfram.com/xid/0n4oikqt8mi-8b8ag6
Out[3]=3
Wolfram Research (2019), InitialSeeding, Wolfram Language function, https://reference.wolfram.com/language/ref/InitialSeeding.html.
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Wolfram Research (2019), InitialSeeding, Wolfram Language function, https://reference.wolfram.com/language/ref/InitialSeeding.html.

Text

Wolfram Research (2019), InitialSeeding, Wolfram Language function, https://reference.wolfram.com/language/ref/InitialSeeding.html.

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Wolfram Research (2019), InitialSeeding, Wolfram Language function, https://reference.wolfram.com/language/ref/InitialSeeding.html.

CMS

Wolfram Language. 2019. "InitialSeeding." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InitialSeeding.html.

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Wolfram Language. 2019. "InitialSeeding." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InitialSeeding.html.

APA

Wolfram Language. (2019). InitialSeeding. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InitialSeeding.html

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Wolfram Language. (2019). InitialSeeding. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InitialSeeding.html

BibTeX

@misc{reference.wolfram_2025_initialseeding, author="Wolfram Research", title="{InitialSeeding}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InitialSeeding.html}", note=[Accessed: 16-April-2025 ]}

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@misc{reference.wolfram_2025_initialseeding, author="Wolfram Research", title="{InitialSeeding}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InitialSeeding.html}", note=[Accessed: 16-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_initialseeding, organization={Wolfram Research}, title={InitialSeeding}, year={2019}, url={https://reference.wolfram.com/language/ref/InitialSeeding.html}, note=[Accessed: 16-April-2025 ]}

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@online{reference.wolfram_2025_initialseeding, organization={Wolfram Research}, title={InitialSeeding}, year={2019}, url={https://reference.wolfram.com/language/ref/InitialSeeding.html}, note=[Accessed: 16-April-2025 ]}