Difficulty solving and plotting solution to complicated second order ODE.

Hi all,

I am trying to solve quite an ODE that I have formed in my attempt to model the removal of a particle from a thin film. In order to solve this, I am trying to make use of the "odeToVectorField" function in order to break down the second order equation into two first order ODE's.

My script seems to work perfectly, where I can form a MATLAB function of the two first order ODE's, however this is unable to be solved when I call ODE45. I am presented with the following error messages:

Index exceeds matrix dimensions.

Error in symengine>makeFhandle/@(Y,t)[Y(2);(Y(2).*(-6.136363636363637e3))./Y(1)+9.810000000000001]

Error in odearguments (line 87) f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 113) [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in furthertests (line 16) sol = ode45(M,[0 20],[1 0]);

I am really not sure why this is occuring. Here is the script that I am currently running:

 clc;
clear; 
D0 = 0.1*10^-9; 
R = 1*10^-6;
m = (4/3)*pi*(R^3)*1100; 
mew = 1.5; 
F0 = m*9.81; 
syms y(t) 
eqn = m.*diff(y,2)== F0 - 6.*pi.*mew.*(R.^2).*(1./y).*diff(y); 
V = odeToVectorField(eqn)
%This breaks down the second order ODE into two separate first order ODE's 
M = matlabFunction(V,'vars',{'Y','t'})
sol = ode45(M,[0 20],[1 0]);
fplot(@(t)deval(sol,t,1), [0, 20])

Apologies for the dodgy spacing in my script, I couldn't figure out how to space it properly on this forum.

Any help you could give with this would be much appreciated.

Cheers.

Answer 1

[Star Strider]

The time (or other independent variable) has to come first in the argument list of ODE functions.

Reverse them and it works:

M = matlabFunction(V,'vars',{'t','Y'})

[Peter]

Ah...thank you so much!

[Star Strider]

As always, my pleasure!