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

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ANDREW CLEMENT 2020-3-7

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评论： darova 2020-3-7

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];

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

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采纳的回答

darova 2020-3-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/509599-how-do-i-use-bvp5c-or-4c-iteratively-to-solve-bvp-for-different-values-of-a-known-parameter#answer_419025

编辑：darova 2020-3-7

在 MATLAB Online 中打开

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 

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ANDREW CLEMENT 2020-3-7

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