MATLAB Mathematics - SERC - Index of

Initial Value Problems for ODEs and DAEs
function hb1dae
%HB1DAE Stiff differential-algebraic equation (DAE)
% A constant, singular mass matrix
M = [1 0 0
0 1 0
0 0 0];
% Use an inconsistent initial condition to test initialization.
y0 = [1; 0; 1e-3];
tspan = [0 4*logspace(-6,6)];
% Use the LSODI example tolerances. The 'MassSingular' property
% is left at its default 'maybe' to test the automatic detection
% of a DAE.
options = odeset('Mass',M,'RelTol',1e-4,...
'AbsTol',[1e-6 1e-10 1e-6],'Vectorized','on');
[t,y] = ode15s(@f,tspan,y0,options);
y(:,2) = 1e4*y(:,2);
semilogx(t,y);
ylabel('1e4 * y(:,2)');
title(['Robertson DAE problem with a Conservation Law, '...
'solved by ODE15S']);
xlabel('This is equivalent to the stiff ODEs coded in HB1ODE.');
% --------------------------------------------------------------
function out = f(t,y)
out = [ -0.04*y(1,:) + 1e4*y(2,:).*y(3,:)
0.04*y(1,:) - 1e4*y(2,:).*y(3,:) - 3e7*y(2,:).^2
y(1,:) + y(2,:) + y(3,:) - 1 ];
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