passing a matrix to ode45: ode45('fna​me',tspan,​matrix,opt​ions)

Hi all,

I am 'recoding' some code written by my professor that integrates a PDE over a 2D lattice.

It appears that he passes the 2D initial condition to ode45() without reshaping it first, and that ode45 automatically reshapes it...I didn't know you could do this? I can't find any documentation on this, but it looks like that is exactly what is happening.

Am I missing something here?

Code:

whos Y0

% confirms 21x21

pause();

[T,Y]=ode45('eqNLS2D_sat',tspan,Y0,options,Nx,Ny);

function [F]=eqNLS2D_sat(t,Y,flag,Nx,Ny)

global C gamma mu V VV LAP;

whos Y

%confirms 441x1

pause();

Y2=Y.*conj(Y);

F=(-LAP*Y+gamma*Y./(1+Y2)+VV.*Y)/1i;

Will

[Andrei Bobrov]

where the code?

Answer 1

[Walter Roberson]

I suspect this is merely standard linear indexing. Every multidimensional array index maps in to a linear array position number. For example, a 4 x 4 array has the following linear indexes:

1 5  9 13
2 6 10 14
3 7 11 15
4 8 12 16

so if you had (for example) the array A

    32    35    11    38
    40     6    30    28
    22     3    33    17
    34    16     7    14

then the "30" could be indexed as A(2,3) or equivalently as A(10)

Nothing special needs to be done to invoke this kind of linear indexing: it happens automatically when an array is indexed with a single index.

[William]

That makes sense.

[RB]

Can we solve matrix differential equations using ode 45 that is equations involving a matrix of unknowns.

Thanks.

[Walter Roberson]

Depending on what is known, that might be a candidate for the boundary value problem routines.

[RB]

Thanks. I have the terminal values but the equation is involving 2*2 matrices.

Solve the following system of ODE's

d/dt Y(t)=-(H(t))^{T}Y(t) 
d/dt V(t)=-Y(t)^{T}Q^{T}QY(t)

with the terminal conditions Y(T)=I_{2} and V(T)=0. Y, V, H and Q are 2*2 matrices.

I am unable to use ode45 since I want matrix result.

It would be great if you can give a suggestion.

\[
H=
  \begin{bmatrix}
    -0.5 & 0.4 \\
    0.007 & -0.008 
  \end{bmatrix}
\]
\[
Q=
  \begin{bmatrix}
    0.06 & -0.0006 \\
    -0.06 & 0.006 
  \end{bmatrix}
\]