I need to solve a simultaneous system of 70,000 ODEs in MATLAB using ode15s but I get the "maximum variable size allowed by the program exceeded" error. Anybody know whether this can be fixed? Or anybody actually has experience solving such large ODE systems? Would appreciate if someone can drop some insights to this?
If you can, try to use sparse matrices.
See brussode - example of large stiff sparse problem.
Just type in the command window:
open brussode
What type of equations are you solving? Is the system of equations linear or nonlinear?
I increased the swap space in my pc, and there may be indications that it is working. Amran, I am solving a system of linear and stiff ODEs.
I haven't have experience solving very large system. Is yours linear autonomous system? I have started another thread asking is there an efficient way to compute large dimension state transition matrix.
Hello Amran, at the moment there are no inputs yet to the model and the model parameters are non-time varying. To be more specific, I am actually trying to simulate the cutting of polymer molecules monomer by monomer and what I am trying to do now is to solve the complete spectrum of polymer cuttings to get the exact (not analytical) solution. After that, I am developing a numerical algorithm to significantly reduce the number of ODEs to be solved and yet obtaining great accuracy to the important state variables that can be measured experimentally. So essentially I am just trying to get the base case for comparisons.
Dear Y K H, Dependently of your function you may select one of the following methods : Explicit Euler , Implicit Euler, Trapeze, Midle point or Adams ....... It is easier to program them for your first order system of ordinary differential equations case. However, you have to analyze the stability of your method in order to ensure that your scheme is stable (numerical stability) for the selected time step.
Hello Yong, I am studying the thermal degradation of polymers and I have a system of homogeneous differential equations with matrix A(t) of non-constant coefficients as in X'(t)= A(t)*x(t).
I have written a simple m file to construct a symbolic system of ODEs, later I used odefunction to pass this system to an ode15s solver. When I have ≈300 equations, the system solves pretty fast. However, when I try to solve 1800 equations (DP=1800) I get an error in Matlab. Have you found a way to rapidly solve your large system?
On the other hand, I have been reviewing other options and I found that the software Predici, based on a Galerkin h-p-method, is capable of dealing with this kind of polymer studies with a large number of ODE equations.
http://www.cit-wulkow.de/products/predici-polymerization
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