Non-uniform grid
3 views (last 30 days)
Show older comments
I have a question about unequal spacing.
In the code below, I would like to either increase the number of N to avoid running out of memory, or increase the number of grids only around i=2N to prevent the solution from diverging.
I use Solve Stiff ODEs https://jp.mathworks.com/help/matlab/math/solve-stiff-odes.html?lang=en
function brussode(N)
if nargin<1
N = 100;
end
tspan = [0; 10]; %時間変更可能
y0 = [repmat(0.9,1,N); repmat(321221,1,N)];
options = odeset('Vectorized','on');
[t,y] = ode15s(@f,tspan,y0,options);
u= y(:,1:2:end);
x = (1:N)/(N+1);
p=y(:,2:2:end);
assignin('base','s',u(end,:))
assignin('base','p',p(end,:))
function dydt = f(~,y)
a=0.0002/N;
b=3.15*10^-4;
c=2.4*10^-5;
d=300000;
e=1;
f=174284;
k=6.4*10^-14;
l=5;
dydt = zeros(2*N,size(y,2)); % preallocate dy/dt
i = 1;
dydt(i,:) = 1/2/a^2/b*((k*(y(i,:).^l+y(i+2,:).^l)).*((y(i+3,:)-y(i+1,:))+f*(1.417*(y(i+2,:)-y(i,:))-2.12*((1-y(i,:)).^2-(1-y(i+2,:)).^2)+1.263*((1-y(i,:)).^3-(1-y(i+2,:)).^3))).*y(i,:)-(k*(2* y(i,:).^l)).*((y(i+1,:)-d)+f*(1.417*(y(i,:)-e)-2.12*((1-e).^2-(1-y(i,:)).^2)+1.263*((1-e).^3-(1-y(i,:)).^3))).*y(i,:));
dydt(i+1,:) =1/2/a^2/c*((k*((1-y(i,:)).^l+(1-y(i+2,:)).^l).*(y(i+3,:)-y(i+1,:))).*y(i+3,:)-(2*k*((1-y(i,:)).^l).*(y(i+1,:)-d)).*y(i+1,:));
% Evaluate the 2 components of the function at all interior grid points.
i = 3:2:2*N-3;
dydt(i,:) = 1/2/a^2/b*((k*(y(i,:).^l+y(i+2,:).^l)).*((y(i+3,:)-y(i+1,:))+f*(1.417*(y(i+2,:)-y(i,:))-2.12*((1-y(i,:)).^2-(1-y(i+2,:)).^2)+1.263*((1-y(i,:)).^3-(1-y(i+2,:)).^3))).*y(i,:)-(k*(y(i-2,:).^l+y(i,:).^l)).*((y(i+1,:)-y(i-1,:))+f*(1.417*(y(i,:)-y(i-2,:))-2.12*((1-y(i-2,:)).^2-(1-y(i,:)).^2)+1.263*((1-y(i-2,:)).^3-(1-y(i,:)).^3))).*y(i-2,:));
dydt(i+1,:) =1/2/a^2/c*((k*((1-y(i,:)).^l+(1-y(i+2,:)).^l).*(y(i+3,:)-y(i+1,:))).*y(i+3,:)-(k*((1-y(i-2,:)).^l+(1-y(i,:)).^l).*(y(i+1,:)-y(i-1,:))).*y(i+1,:));
i = 2*N-1;
dydt(i,:) = 1/2/a^2/b*(-9.93*10^-6*a*b*2-(k*(y(i-2,:).^l+y(i,:).^l)).*((y(i+1,:)-y(i-1,:))+f*(1.417*(y(i,:)-y(i-2,:))-2.12*((1-y(i-2,:)).^2-(1-y(i,:)).^2)+1.263*((1-y(i-2,:)).^3-(1-y(i,:)).^3))).*y(i-2,:));
dydt(i+1,:) =1/2/a^2/c*(804./y(i,:) *a*c*2-(k*((1-y(i-2,:)).^l+(1-y(i,:)).^l)).*(y(i+1,:)-y(i-1,:)).*y(i+1,:));
end
end
Please let me know what I need to change to calculate under 300GB.
Thank you for your help.
1 Comment
John D'Errico
on 9 Mar 2022
Why are you using a hack like assignin, instead of just returning the variables as arguments from the function?
Answers (0)
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!