Matlab ode45. How to change a parameter inside it while calling it?
You want make F an argument of your derivative function and pass the right anonymous function to ode45: [t,N] = ode45(@(t,y) rateEquations(t,y,F), timeSpan, initialConditions)
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Solving an ODE when the function is given as discrete values -matlab-
You can use interp1 to create an interpolated lookup table function: fx = [0.5644 0.6473 0.7258 0.7999 0.8697 0.9353 0.9967 1.0540 1.1072 1.1564 … 1.2016 1.2429 1.2803 1.3138 1.3435 1.3695 1.3917 1.4102 1.4250 1.4362 … 1.4438 1.4477 1.4482 1.4450 1.4384 1.4283 1.4147 1.3977 1.3773 1.3535 … 1.3263 1.2957 1.2618 1.2246 1.1841 1.1403 1.0932 1.0429 0.9893 … Read more
Error in RK4 algorithm in Python
Two different errors were obvious in the first parsing. (was not an error, ifft is indeed the complete inverse of fft. This might not be the case in other libraries.) In the RK4 step, you have to decide on one place for the factor h. Either (as example, the others analogously) k2 = f(t+0.5*h, y+0.5*h*k1) … Read more
Absolute error of ODE45 and Runge-Kutta methods compared with analytical solution
Your RK4 function is taking fixed steps that are much smaller than those that ode45 is taking. What you’re really seeing is the error due to polynomial interpolation that is used to produce the points in between the true steps that ode45 takes. This is often referred to as “dense output” (see Hairer & Ostermann … Read more
MATLAB: Is it possible to have two event values whilst using ode45?
I’m not sure if you can do exactly what you want, but it is possible to do quite a lot with events. First, this sounds like some sort of numerical calculation of first passage time (a.k.a first hitting time). If these “particles” are stochastic, stop and don’t use ode45 but rather a a method appropriate … Read more
Matlab ode solvers: changing state and specified time
Inserting large discontinuities in your ODE in the way you suggest (and the way illustrated by @macduff) can lead to less precision and longer computation times (especially with ode45 – ode15s might be a better option or at least make sure that your absolute and relative tolerances are suitable). You’ve effectively produced a very stiff … Read more