Imagine I have the following non linear problem in discrete time, where z is a exogeneous signal:
To solve it, and, not wanting or not able to inverse the equation, I'd like to use a numerical solver. Given x[t-1] and z[t]; it is starighfoward to solve for x[t] and thus being able to simulate the following discrete equation where f~ stand for the inverse of the inital function (x-sqrt(x+z)):
In odin, may be such non linearity could be detected or written explicitly by the user:
Imagine I have the following non linear problem in discrete time, where z is a exogeneous signal:
To solve it, and, not wanting or not able to inverse the equation, I'd like to use a numerical solver. Given x[t-1] and z[t]; it is starighfoward to solve for x[t] and thus being able to simulate the following discrete equation where f~ stand for the inverse of the inital function (x-sqrt(x+z)):
In odin, may be such non linearity could be detected or written explicitly by the user:
odin({ solve({ update(x) <- x + sqrt(update(x) + z[step] }, x)I think that with continuous time, there is not such a problem as the equation can be written this way: