Dear Etiene Ubeh,
Yes, parameter estimations methods are suitable to do so. There are many works about this topic in the literature. There also also several tool box in Matlab for this purpose. However, i think that SSm is the best algorithm to do so. please see the attached paper.
http://www.mathworks.com/discovery/parameter-estimation.html
why parameter estimation? there are ode solvers in matlab for this and in R as well, for instance http://it.mathworks.com/help/matlab/math/ordinary-differential-equations.html
Dear Etiene Ubeh
You can applied The Runge-Kutta Method, for more detail see :
- https://www.youtube.com/watch?v=kUcc8vAgoQ0
- http://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node5.html
- http://www.math.tamu.edu/~phoward/m442/matode.pdf
- https://www.youtube.com/watch?v=kUcc8vAgoQ0
That depends on your ODE, Euler can underestimate curvature because of the simple projection scheme; hence Maghnia's comment to use a higher order integration scheme (Matteo's suggestion to use Matlab's ODE solver is nice because they will adjust the step-size for you--assuming you want such automation).
You can use the new method presented in:
Katsikadelis, J.T. "A NEW DIRECT TIME INTEGRATION METHOD FOR THE SEMI-DISCRETE PARABOLIC EQUATION", 8th GRACM International Congress on Computational Mechanics, Volos, Greece, 12 July – 15 July 2015
The method is very efficient, unconditionally stable, converge energy and very simple to implement.
You can download the paper from Katsikadelis' Research-gate webpage. The journal paper will appear in due time.
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