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[an error occurred while processing this directive] SolvePDE

  • SolvePDE[ eqns , y , { x , xmin , xmax } ] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range xmin to xmax .
  • SolvePDE[ eqns , y , { x , xmin , xmax } , { t , tmin , tmax } ] finds a numerical solution to the partial differential equations eqns .
  • SolvePDE[ eqns , { , , ... } , { x , xmin , xmax } ] finds numerical solutions for the functions .
  • SolvePDE gives results in terms of InterpolatingFunction objects.
  • SolvePDE[ eqns , y [ x ], { x , xmin , xmax } ] gives solutions for y [ x ] rather than for the function y itself.
  • SolvePDE solves a wide range of ordinary differential equations, and some partial differential equations.
  • In ordinary differential equations, the functions must depend only on the single variable x . In partial differential equations, they may depend on more than one variable.
  • The differential equations must contain enough initial or boundary conditions to determine the solutions for the completely.
  • Initial and boundary conditions are typically stated in form y [ ] == , y '[ ] == , etc., but may consist of more complicated equations.
  • The point that appears in the initial or boundary conditions need not lie in the range xmin to xmax over which the solution is sought.
  • The differential equations in SolvePDE can involve complex numbers.
  • See also: D , Integrate , ND , NIntegrate , SolveEquation .


    Examples

    Using InstantCalculators

    Here are the InstantCalculators for the SolvePDE function. Enter the parameters for your calculation and click Calculate to see the result.

    In[1]:=

    Out[1]=

    In[2]:=

    Entering Commands Directly

    You can paste a template for this command via the Text Input button on the SolvePDE Function Controller.

    In[3]:=

    Out[3]=



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