ODEs: 3 approaches: which is best?

[Jim H]

I know of at least 3 ways to solve odes using lsode and I did a simple
tic-toc comparison.  I'd like to know what users think are the pro's and
con's of the different approaches.

Method 1: put the function to be integrated in one file and run it from
another file
Method 2: put the function in a file with the lsode invocation + put the
parameters inside the function
Method 3: Method 2, but pass the parameters to the function.

Simple Timings: average of 3
Method 1: 2.13 sec
Method 2: 2.19 sec
Method 3: 2.59 sec

Is (1) fastest because of compiling? Why is (2) faster than (3)? But, speed
is not everything; there is something to be said for having 1 file,
especially in the context of teaching modeling to biologists.  Any opinions
on advantages and disadvantages?

-Jim

Here are the basic codes...
=======================
Method (1) Run file:
%Parameters (model specific)
global    ALF    =     1.5;         % competition N1 on N2            
global    B      =    0.01;         % predation rate                  
global    C      =    0.5;          % conversion Prey to Predator     
global    D      =    1.0;          % predator death rate             
global    EP     =    0.009;        % N2 predator avoidance advantage 
global    K      =    800;          % N(1)(2) carrying capacity       
global    R      =    1.0;          % prey percapita increase         

global MODEL="OSimVanceFunc";
    yo = [200; 200; 40];
    t=linspace(0,1200,1201);
tic()
    y=lsode(MODEL,yo,t);
toc()

Method (1) Function File:
function dydt = OSimVanceFunc(y,t)
global    ALF;       % competition N1 on N2            
global    B  ;       % predation rate                  
global    C  ;       % conversion Prey to Predator     
global    D  ;       % predator death rate             
global    EP ;       % N2 predator avoidance advantage 
global    K  ;       % N(1)(2) carrying capacity       
global    R  ;       % prey percapita increase         
    n1 =  y(1)*(R - (R/K)*(y(1)+y(2)) - B*y(3));
    n2 =  y(2)*(R - (R/K)*(ALF*y(1)+y(2)) -(B-EP)*y(3));
    n3 =  y(3)*(C*B*y(1) + C*(B-EP)*y(2) - D);
    dydt = [n1;n2;n3];
====================================
Method (2) 
1;  % dummy command so we can have a function defined in this file
function ret = f(x,t)
 ALF    =     1.5;         % competition N1 on N2
 B      =    0.01;         % predation rate 
 C      =    0.5;          % conversion Prey to Predator
 D      =    1.0;          % predator death rate
 EP     =    0.009;        % N2 predator avoidance advantage
 K      =    800;          % N(1)(2) carrying capacity
 R      =    1.0;          % prey percapita increase
 
% the model
    n1 =  x(1)*(R - (R/K)*(x(1)+x(2)) - B*x(3));
    n2 =  x(2)*(R - (R/K)*(ALF*x(1)+x(2)) -(B-EP)*x(3));
    n3 =  x(3)*(C*B*x(1) + C*(B-EP)*x(2) - D);
    ret = [n1;n2;n3];
endfunction 
 
x0  = [200;200;40];         % initial conditions as column vector
t=linspace(0,1200,1201)';     % solution times as column vector
tic()
x=lsode("f",x0,t);          % solve
toc()
==================================================
Method (3)
1;  % dummy command so we can have a function defined in this file
function ret = f(x,t, ALF,B,C,D,EP,K,R)
% the model
    n1 =  x(1)*(R - (R/K)*(x(1)+x(2)) - B*x(3));
    n2 =  x(2)*(R - (R/K)*(ALF*x(1)+x(2)) -(B-EP)*x(3));
    n3 =  x(3)*(C*B*x(1) + C*(B-EP)*x(2) - D);
    ret = [n1;n2;n3];
endfunction 

 ALF    =     1.5;         % competition N1 on N2
 B      =    0.01;         % predation rate 
 C      =    0.5;          % conversion Prey to Predator
 D      =    1.0;          % predator death rate
 EP     =    0.009;        % N2 predator avoidance advantage
 K      =    800;          % N(1)(2) carrying capacity
 R      =    1.0;          % prey percapita increase
x0  = [200;200;40];         % initial conditions as column vector
t=linspace(0,1200,1201)';     % solution times as column vector
g = @(x,t) f(x, t, ALF, B, C, D, EP, K, R);
tic()
x=lsode(g, x0, t);
toc()

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