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I am trying to get a solution for a stiff ODE problem where at each integration step, i have to modify the solution vector before continuing on the integration. For that, i am using scipy.integrate.ode, with the integrator VODE, in bdf mode. Here is a simplified version of the code i am using. The function is much more complex than that and involve the use of CANTERA.

I'm attempting to solve a set of equations related to biological processes. One equation (of about 5) is for a pharmacokinetic (PK) curve of the form C = Co(exp(k1*t)-exp(k2*t). The need is to simultaneously solve the derivative of this equation along with some enzyme binding equations and initial results where not as expected. After troubleshooting, realized that the PK derivative doesn't numerically integrate by itself, if k is negative using the desolve ode function. I've attempted every method (lsode, lsoda, etc) in the ode function, with no success. I've tried adjusting rtol, it doesn't resolve.

Is there an alternative to the deSolve ode function I should investigate? Or another way to get at this problem?

Below is the code with a simplified equation to demonstrate the problem. When k is negative, the integrated solution does not match the analytical result. When k is positive, results are as expected.

First Image, result with k=0.2: Analytical and Integrated results match when k is positive

Second Image, result with k=-0.2: Integrated result does not match analytical when k is negative

So I am trying to solve the following system of differential equations in Python.

System of differential equations

As you can see, for each n in {0,1,2,3,...} the system depends on the solution to the previous system.

I have tried solving the system for n=0 and found a solution R(0|t) that I can insert in R(1|t) and Python solves the system without problems. I have defined the solution R(0|t) as r0(t) and implemented the solution for n=1 as follows:

I am trying to establish a method of estimating infectious disease parameters by comparing real epidemic curves with simulations of a stochastic SIR model. To construct the stochastic SIR model, I am using the deSolve package and instead of using fixed parameter values I would like to draw the parameter value used in the equations at each time point from a Poisson distribution centered on the original parameter values.

Using the parameter beta as an example, beta represents the average number of transmission events per capita and is the product of the average number of contacts and the probability that transmission occurs upon contact. Realistically, there is variation in the number of contacts a person will have and since transmission is also a probabilistic event there is variation surrounding this too. So even if the average transmission rate were to be 2.4 (for example), an individual can go on to infect 0, 1, 2 or 3 ... etc. people with varying probabilities.

I have tried to incorporate this into my code below using the rpois function and reassigning the parameters used in the equations to the outputs of the rpois.

I have run my code with the same initial values and parameters multiple times and all the curves are different indicating that SOMETHING "stochastic" is going on, but I am unsure whether the code is sampling using the rpois at each time point or just once at the beginning. I have only started coding very recently so do not have much experience.

I would be grateful if anyone more experienced than myself could verify what my code is ACTUALLY doing and whether it is sampling using rpois at each time point or not. If not I would be grateful for any suggestions for achieving this. Perhaps a loop is needed?

I am struggling with a probably minor problem while calling compiled ODEs to be solved via the R package 'deSolve' and I seeking advice from more expert users.

I have a couple of ODE systems to be solved with 'deSolve'. I have defined the ODEs in separate C++ functions (one for each model) I am calling through R in conjunction with 'Rcpp'. The initial values of the system change if the function takes input from another model (so basically to have a cascade).

This works quite nicely, however, for one model I have to set the initial parameters for t < 2. I've tried to do this in the C++ function, but it does not seem to work.

I am trying to solve a 1D PDE coupled with an ODE (solved as explicit Euler). I am getting a stack-overflow error if I use small dt. I tried looking at the length of the stack but cannot figure out anything useful from there. I am not very experienced with python (old fortran numerics coder).
The code:

I'm currently exploring the Lorenz system with Python and R and have noticed subtle differences in the ode packages. odeint from Python and ode both say they use lsoda to calculate their derivatives. However, using the lsoda command for both seems to give far different results. I have tried ode45 for the ode function in R to get something more similar to Python but am wondering why I can't get exactly the same results:

I am trying to get the button to do a single alert when the button is clicked, but the button odes something strange:

The first time I click the Login Button, the alert shows once, when I click it again the alert shows 2 times, then I click the button a 3rd time, the alert shows 3 times. After that, If I were to click the Forgot Password Button, the alert assigned to Forgot password would show 4 times.

I am very confused as to why this happens and how to fix it?

.ts

I'd like to simulate this system of equations in a matlab program.

I'm need help to set up the code. I have a Matlab function for doing Runge-Kutta4k approximation for first-order ODE's, and I want to adapt it to work for second-order ODE's.

Here's some code :

RK4 function: