How do I use BVP5c (or 4c) iteratively to solve BVP for different values of a known parameter

I have managed to solve a system of 4 (first-order autonomous) ODE's subject to 7 boundary conditions and for fixed values of my known parameter g. However, now I want to vary g and plot the different curves. Originally I specified the value of g inside my ODE and ODE_bc functions (see below) - e.g. I may write g=1; just below where I specified my unknown parameter r. However, now it seems that I need to specify g outside my functions in order to iterate over different values of g (using a for loop) and using the code below I get the error:

Error using bvp5c

Too many input arguments.

Error in Iterated_ODE (line 4)

sol1 = bvp5c(@simp_ODE,@simp_bc,solinit1,options,g);

I've tried taking the 4th argument g out entirely for the simp_ODE and simp_bc and then for the 5th argument in BVP5c (above) but with no success.

How can I correct this problem?

(see current code below)

options = bvpset('stats','on');

g = 1;

solinit1 = bvpinit(linspace(0,1,20),@ODE_init,[0.75 -0.7 1.47]); %initial guess

sol1 = bvp5c(@simp_ODE,@simp_bc,solinit1,options,g);

sol = bvp5c(@ODE,@ODE_bc,sol1,options,g);

plot(sol.y(1,:),sol.y(3,:)); %plots y(3)=theta vs y(1)=x $

axis equal

hold on

for i=1:10

g = g+0.5; %Increment known/prescribed parameter

sol = bvp5c(@ODE,@ODE_bc,sol,options); %use previous solution as inital guess

plot(sol.y(1,:),sol.y(3,:)); %plots y(3)=theta vs y(1)=x $

axis equal

hold on

end

function G = ODE_init(s)

G = [s %guess x(s) = s%

0

0

0];

end

function dydx = simp_ODE(x,y,array, g) %first-order simplified ODE using cos(x) = 1+O(x), sin(x)=x+O(x^3)%

b = array(1);

n=array(2);

r = array(3);

dydx = [x

y(2)

y(3)

n*y(2)-g*(x+y(1)*y(2))/r]; % b,n,r are unknown parameters to solve for%

end

%tried to specify unknown parameters using array and g is a known parameter%

function res = simp_bc(ya,yb,array,g) %bc's to simplified ODE using a 'first order approximation%

b = array(1) ;

n = array(2);

r = array(3);

res = [ya(1) %x(0)=0%

ya(2) %y(0) = 0%

ya(3) %theta(0) = 0%

yb(4) %psi(1) = theta'(1) =0 in non-dim bc%

yb(3)+b-pi/3 %Wetting angle relation at boundary theta(1)+beta = pi/6%

1 - r*sin(b) %geometric condition%

yb(2) - r*(n +cos(b))]; %internal force y(1) -r*n-r*cos(b) == 0%

end

function dyds = ODE(s,y,array,g)

b = array(1);

n = array(2);

r = array(3);

% g = 1;

dyds = [cos(y(3));

sin(y(3));

y(4);

n*sin(y(3))-g*(y(1)+y(2)*sin(y(3)))/r];

end

function res = ODE_bc(ya,yb,array,g)

b = array(1) ;

n = array(2);

r = array(3);

res = [ya(1) %x(0)=0%

ya(2) %y(0) = 0%

ya(3) %theta(0) = 0%

yb(4) %psi(1) = theta'(1) =0 in non-dim bc%

yb(3)+b-pi/3 %Wetting angle relation at boundary theta(1)+beta = pi/6%

yb(1) - r*sin(b) %geometric condition%

yb(2) - r*(n +cos(b))]; %internal force bc y(1) -r*n-r*cos(b) == 0%

end

Answer 1

[darova]

Passing extra parameters

 sol = bvp5c(@(x,y)ODE(x,y,ar,g),@(a,b)ODE_bc(a,b,ar,g),sol,options);  %use previous solution as inital guess 

[ANDREW CLEMENT]

I'm afraid that hasn't worked. It has come up with 2 red errors which stop the function from running. One is a 'parse error' with the parenthesis and another saying 'cannot call or index into a temporary array'.

[darova]

Sorry, didn't see array is vector of uknown

Try

sol1 = bvp5c(@(x,y,ar)simp_ODE(x,y,ar,g), ...
            @(a,b,ar)simp_bc(a,b,ar,g),solinit1,options);
sol = bvp5c(@(x,y,ar)ODE(x,y,ar,g), ...
            @(a,b,ar)simp_bc(a,b,ar,g),sol1,options);

[ANDREW CLEMENT]

I've already tried that and it gives the same errors :/

[darova]

I suppose that you changed these?

[ANDREW CLEMENT]

I have changed the top part of my code to the following (changes in bold):

options = bvpset('stats','on');

g=1;

solinit1 = bvpinit(linspace(0,1,20),@ODE_init,[0.75 -0.7 1.47]);

sol1 = bvp5c(@simp_ODE, @simp_bc,solinit1,options);

sol = bvp5c(@(x,y,ar)@ODE(x,y,ar,g),@(a,c,ar)@ODE_bc(a,c,ar,g),sol1,options);

plot(sol.y(1,:),sol.y(3,:)); %plots y(3)=theta vs y(1)=x $

axis equal

hold on

for i=1:10

g = g+0.5;

sol = bvp5c(@(x,y,ar)@ODE(x,y,ar,g),@(a,b,ar)@ODE_bc(a,b,ar,g),sol,options);

plot(sol.y(1,:),sol.y(3,:)); %plots y(3)=theta vs y(1)=x $

axis equal

hold on

end

[darova]

What error says?

[ANDREW CLEMENT]

Error: File: Iterated_ODE.m Line: 5 Column: 23

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

[darova]

Can you show this line?

[ANDREW CLEMENT]

sol = bvp5c(@(x,y,ar)@ODE(x,y,ar,g),@(a,c,ar)@ODE_bc(a,c,ar,g),sol1,options);

[darova]

Try to change this line

sol1 = bvp5c(@(x,y,ar)simp_ODE(x,y,ar,g), ...
             @(a,b,ar)simp_bc(a,b,ar,g),solinit1,options);

[ANDREW CLEMENT]

No luck I'm afraid. Same error in the line that says:

sol = bvp5c(@(x,y,ar)@ODE(x,y,ar,g),@(a,c,ar)@ODE_bc(a,c,ar,g),sol1,options);

[ANDREW CLEMENT]

Actually that final suggestion gave me an idea. I'm not sure if you meant to omit the @ symbols before the functions but it gave me no error on that line so I tried in all the lines using BVP5c and it worked! Thank you very much for your help

[darova]