InitialData - Maple Help

InitialData

finds the initial data of a LHPDE object

 Calling Sequence InitialData( obj, opts) Initialdata( obj, opts)

Parameters

 obj - a LHPDE object opts - (optional) sequence of options to control the behaviour of DEtools[initialdata]

Description

 • The InitialData method is a front-end to the existing command DEtools[initialdata], which accepts a LHPDE object as the first input argument.
 • All optional arguments will be passed down to DEtools[initialdata].
 • Let S be a LHPDE object then InititalData(S, opts) is equivalent to DEtools[initialdata](GetSystem(S), GetDependents(S), opts).
 • The method name Initialdata is provided as an alias.
 • This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left\{\mathrm{ξ},\mathrm{η},\mathrm{α},\mathrm{β}\right\}\left(x,y\right)\right):$
 > $S≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)=-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{ξ},\mathrm{η}\right]\right)$
 ${S}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $\mathrm{InitialData}\left(S\right)$
 ${table}{}\left(\left[{\mathrm{Infinite}}{=}\left[\right]{,}{\mathrm{Finite}}{=}\left[{\mathrm{\xi }}{}\left({{x}}_{{0}}{,}{{y}}_{{0}}\right){=}{\mathrm{_C1}}{,}{{\mathrm{D}}}_{{2}}{}\left({\mathrm{\xi }}\right){}\left({{x}}_{{0}}{,}{{y}}_{{0}}\right){=}{\mathrm{_C2}}{,}{\mathrm{\eta }}{}\left({{x}}_{{0}}{,}{{y}}_{{0}}\right){=}{\mathrm{_C3}}\right]\right]\right)$ (2)

Compatibility

 • The InitialData command was introduced in Maple 2020.