MATLAB: Ode15s

function handleMATLABodeode15spde

Solving a partial differential equation with ode15s,we know that this ode solver integrates the ode over time direvatives.I need to find the values of these time direvatives,do you have any special command? for example: for i=1:n dudt=uxx(i) end

how can I find these dudt at each time and x(i)? thanks alot

Best Answer

If you are solving something like

[t,x] = solver(odefun,tspan,y0)

and you want the time derivative at each point t(i), then that is simply

dxdt = 0*x;  % initialize the array
for ii=1:length(t)
  dxdt(ii,:) = odefun(t(ii),x(ii,:));
end

(edited to allow for the possibility that x has more than one component at each time t).

Related Solutions

MATLAB: Ode 45 in a loop

You have a couple of problems with your code. Your ode_research does not follow the ordinary form (dydy = ode_f(t,y)) that ode45 expects. Then your use of a string for the first argument is a bit arcane. I would expect something like this would be better:

t = linspace(1,10);
vf(1) = 30 ; %some random constant value
vfx = vf(1); % needed in the function ode_research_x
x(1) = -3;% starting point for x
vp = v_initial; % or whatever you have as initial condition
for i = 1:length(t)-1
    vfx = vf(1); % this vfx is then used by the ode_research_x function
    [tx,vx] = ode45(@(t,vx) ode_research_x(t,vx,vfx), t(i:i+1), vp(1)); % I am not sure but the time step seems like an issue
    x(i+1) =  x(i) + vx(end).*tx;
    vp(1) = vx;
    vf(1) = 30; % some new constant value calculated in the loop (I've shown a random value)
end
%function to define the ode
function dudt = ode_research_x(t,vx,vfx)
% Some initialization of the constants, I assume.
dudt = 18*mu_f*Cd*Rep*(vx - vfx)/(rho_p*d^2*24); % all the variables except vx and vfx are constant values in the same workspace so I haven't shown their values but they are defined 
end

This looks like some attemt to integrate an equation of motion, if that is the case this is not a good way to go about it. In that case you should integrate the second-order ODE (i.e. the two coupled first order-ODEs) and handle the evolution of the force inside the ode_research_x - function.

HTH

MATLAB: How to use ode23s to solve heat equation

If you are still interested in a solution for your problem:

Choose

u(x)=1/eps*max(1-abs(x/eps),0)

for eps=0.001, e.g. as initial condition for your Problem (this is an approximation to the Dirac Delta function).

Choose a very fine grid around x=0 such that the initial guess function is sufficiently resolved.

Then write the usual ODEs that result from

ut=D*uxx

and solve them using ODE15s.

If needed, I could also give you the analytical solution for comparison.

Best wishes

Torsten.

Best Answer

Related Solutions

MATLAB: Ode 45 in a loop

MATLAB: How to use ode23s to solve heat equation

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