initialdata  find initial data for a solvedform ODE or PDE system
initialdata( system )
initialdata( system , vars )
initialdata( rifresult )
initialdata( rifresult , vars )
Parameters
system  list or set of polynomially nonlinear PDEs or ODEs in solved form
vars  the dependent variables to compute the initial data with respect to
rifresult  a single case result as returned by rifsimp
> sys:=[diff(f(x,y),x,x,x)=0,diff(f(x,y),x,y)=0];
3 2
d d
sys := [ f(x, y) = 0,  f(x, y) = 0]
3 dy dx
dx
> initialdata(sys);
table([Finite = [D[1](f)(x[0], y[0]) = _C1, D[1, 1](f)(x[0], y[0]) = _C2],
Infinite = [f(x[0], y) = _F1(y)]
])
> d1:=[3,0],[4,0],[3,1],[4,1],[3,2],[4,2],[3,3],[4,3],[3,4],[4,4]:
> plot([d1], x=0.1..4.1, y=0.1..4.1, style=point,
xtickmarks=[0,1,2,3,4], ytickmarks=[0,1,2,3,4]);
4 + H H



3 + H H



2 + H H



1 + H H



+++**
 1 2 3 4
> d2:=[1,1],[2,1],[3,1],[4,1],[1,2],[2,2],[3,2],[4,2],[1,3],[2,3],
[3,3],[4,3],[1,4],[2,4],[3,4],[4,4]:
> plot([d1,d2], x=0.1..4.1, y=0.1..4.1, style=point,
xtickmarks=[0,1,2,3,4], ytickmarks=[0,1,2,3,4]);
4 + A A A A



3 + A A A A



2 + A A A A



1 + A A A A



+++**
 1 2 3 4
>
with(Rif):
sys1:=[diff(f(x,y,z),x,x)=0,diff(f(x,y,z),y)=0,diff(f(x,y,z),z)=0];
This system is fully specified if the following derivatives are known.
> initialdata(sys1);
For this next system, the initial data contains a number of arbitrary functions of one variable.
>
sys2:=[diff(f(x,y,z),x,y)=0,diff(f(x,y,z),x,z)=0,
diff(f(x,y,z),y,z)=0];
> initialdata(sys2);
For the next system, the initial data contains a number of arbitrary functions of two variables.
> sys3:=[diff(f(x,y,z),x,y,z)=0];
> initialdata(sys3);
Of course, we must include the onedimensional heat equation.
> sys4:=[diff(u(x,t),t)=diff(u(x,t),x,x)];
> initialdata(sys4);
This example is a system that contains mixed data:
> sys5:=[diff(f(x,y,z),x,y,y)=0,diff(f(x,y,z),x,z)=0,diff(f(x,y,z),y,z,z)=0];
> initialdata(sys5);
And an example of use of initialdata with a nonlinear rif result:
> sys6:=[diff(u(x),x,x)^2*u(x)+diff(u(x),x)^3];
> rif6:=rifsimp(sys6);
> initialdata(rif6);
where it is understood that the selected initial data must obey the nonlinear constraint (so in truth we only have two free parameters) and must not violate the pivots (so _C3<>0 , and as a result _C2<>0 ).
caseplot , rifsimp , rtaylor