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Given a set of ODE's $ dot{z} = f(z) $ (or discrete time $ z_{t+1} = f(z_t) $), is there a way to numerically find constants of motion? For $...
Asked on 10/23/2021
3 answerI am trying to solve a system of non-linear index-1 DAEs in which the derivatives of the state variables, $x(t)$ are corrupted by additive noise, $w(t)$ (whose co-variance matrix is...
Asked on 10/23/2021
1 answerFor using any programming language, a mathematical formula should be written in the corresponding code. I wonder if there is any service (for any programming language, Matlab, Mathematica, Python, etc)...
Asked on 10/23/2021
2 answerThe equation and its meaning: Consider two sets $(A)_{l=0,...,m_a},$,$(B)_{l=0,...,m_b}$ of hermitian matrices and a set of positive semidefinite matrices $(C)_{l=0,...,m_c}$. Each matrix has the dimension $n times n$. These form...
Asked on 10/23/2021 by BlueLemon
1 answerThis question is a continuation ofFourth order IMEX Runge-Kutta method, concerning the implementation. Is seems to me that the first implicit stage value involves a direct evaluation, rather...
Asked on 10/23/2021
1 answerI am looking for numerical packages (ideally Python) to solve second kind Volterra integral equations, such as $$u(t)=g(t)+int_0^tK(t,s)u(s) ds$$ or Volterra-Fredholm integral equations $$u(x,t)=g(t,x)+cint_0^tint_Omega K(t,s,x,xi)u(s,xi) dxi ds$$ Are there any...
Asked on 10/23/2021
1 answerI need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation...
Asked on 10/23/2021
2 answerI have these three differential equations in which I need to solve numerically: $$frac{dn_0}{dt}= -n_0(t)W_{01}(t) + n_1(t)K_{10}$$ $$frac{dn_1}{dt}= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{21} + n_0(t)W_{01}(t)...
Asked on 10/23/2021
1 answerI have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher...
Asked on 10/23/2021
1 answerWhat is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?...
Asked on 10/23/2021
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