- Have a read in the documentation of bvp4c
- Try to implement your model with a single fixed value for r and get a valid solution
- Once you have this, use a for loop to vary r like needed for your purposes and save all the results in a Matrix in different columns or rows
- Plot the results by using the saved values
how to write matlab bvp4c code for moving boundary surface problem?
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hello, I am new in the bvp4c method of Matlab. I want to find multiple graphs for different value of 'r' for the following problem. Equation is f''' +ff''=0 Boundary condition is f(0)=0, f'(0)=1-r, f'(infnty)=r
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Accepted Answer
Stephan
on 6 Nov 2018
Edited: Stephan
on 6 Nov 2018
Hi,
i recommend to start simple and work step by step:
Problems by doing this? --> Come back and ask a specific question including your code so far.
Best regards
Stephan
2 Comments
More Answers (1)
Torsten
on 7 Nov 2018
Edited: Torsten
on 7 Nov 2018
function main
r=[0 0.02 0.04]
for i=1:numel(r)
r_actual = r(i);
solinit = bvpinit(linspace(0,10,10000),[0 1-r_actual 0]);
options = bvpset('stats','on');
sol{i} = bvp4c(@equation,@(y0,yinf)bvpbc(y0,yinf,r_actual),solinit,options);
end
for i=1:numel(r)
eta = sol{i}.x;
u = sol{i}.y;
plot(eta,u(3,:));
hold on;
end
end
% --------------------------------------------------------------------------
function dy=equation(~,y)
%dy=zeros(4,1);
dy=[y(2);
y(3);
-y(1)*y(3);
%---------------------------------------------------------------------
];
end
function res = bvpbc(y0,yinf,r_actual)
res = [y0(1)
y0(2)-1+ r_actual
yinf(2)- r_actual
];
end
3 Comments
Torsten
on 7 Nov 2018
Edited: Torsten
on 7 Nov 2018
Try this code - it uses the solution of the last step as initial guess for the next:
function main
global ix
r=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0];
r_actual = r(1);
ir=1;
solinit = bvpinit(linspace(0,10,1000),@(x)guess(x,ir,[0 1-r_actual r_actual]));
options = bvpset('stats','on');
ix = 0;
sol{1} = bvp4c(@equation,@(y0,yinf)bvpbc(y0,yinf,r_actual),solinit,options);
for ir=2:numel(r)
r_actual = r(ir);
solinit = bvpinit(sol{ir-1}.x,@(x)guess(x,ir,sol{ir-1}.y));
options = bvpset('stats','on');
ix = 0;
sol{ir} = bvp4c(@equation,@(y0,yinf)bvpbc(y0,yinf,r_actual),solinit,options);
end
for ir=1:numel(r)
eta = sol{ir}.x;
u = sol{ir}.y;
plot(eta,u(3,:));
hold on;
end
end
% --------------------------------------------------------------------------
function dy=equation(~,y)
%dy=zeros(4,1);
dy=[y(2);
y(3);
-y(1)*y(3);
%---------------------------------------------------------------------
];
end
function res = bvpbc(y0,yinf,r_actual)
res = [y0(1)
y0(2)-1+ r_actual
yinf(2)- r_actual
];
end
function yini=guess(x,ir,sol)
global ix
ix = ix + 1;
if ir==1
yini(1)=sol(1);
yini(2)=sol(2);
yini(3)=sol(3);
else
yini(1)=sol(1,ix);
yini(2)=sol(2,ix);
yini(3)=sol(3,ix);
end
end
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