All Questions
17
questions
4
votes
1
answer
136
views
Findroot :unable to find a solution that meets the convergence criteria
The stationary solutions of the Klein-Gordon equation refer to time-independent solutions, meaning they remain constant over time. For the non-linear Klein-Gordon equation, you are discussing:$$\frac{...
2
votes
0
answers
218
views
Solving `Integrate` of `InterpolatingFunction` from an `NDSolve`
I am interested in solving a system of Differential Equations, particularly
u''[\[Tau]]=-f[t]u[\[Tau]]
This system has for initial conditions $u(0)=1/\sqrt{2\cdot ...
1
vote
0
answers
225
views
Help with code for impulsive optimal control problem
I am using Mathematica 13.3 to numerically solve/generate numerical plots for my impulsive control problem.
The optimal control problem is:
T is time from0 to T where T is the terminal time
K(t), B(t) ...
- 11
0
votes
0
answers
54
views
Finding values of constants for which 1st and 2nd order derivatives of a function vanish
I'm trying to find critical values of some constants $v_c$ and $T_c$, for which holds the equality below:
$$\bigg(\frac{\partial P}{\partial v}\bigg)\biggr\rvert_{v=v_c,\; T=T_c}=0,\quad \bigg(\frac{\...
- 27
1
vote
2
answers
323
views
Mathematica: How can I solve the problem "The Kernel Local has quit (exited) during the course of an evaluation"
I am using a Mac Book with Monterey and 16GB RAM for a calculation with 2 nested For loops.
I am relatively new to Mathematika and still trying to learn the language properly, so I hope the problem is ...
10
votes
2
answers
1k
views
Problem with optimal control and Pontryagin's maximum principle
For dynamic system:
$\dot{x}=\frac{df}{dx}+u$
where $f=e^{-x^2}$
It is necessary to develop optimal control, minimizing criterion:
$J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $
Algorithm:
We ...
- 2,444
1
vote
1
answer
99
views
Optimization of second order ODE with more than one parameter
I want to optimize a second order ODE with more than one variable:
...
- 91
2
votes
2
answers
219
views
Minimization using NMinimize
I have a system of ODEs say
$$x'(t)=2 x(t)-x(t)y(t)-3 x(t) g(t),$$
$$y'(t)= y(t)-2 x(t)y(t)- x(t) g(t)$$
with ICs $x(0)= 1, y(0)=1/2$, say, for $t_0 \leqslant t \leqslant t_f$, where $t_0$ and $t_f$ ...
- 21
0
votes
0
answers
175
views
Problem in solving system of equations using "Solve"
I have an equation in its normalized form as:
$\frac{v(x)}{V_{cc}}=C_1\cos qx+C_2\sin qx+1+ \frac{q^2}{1-q^2}.\frac{V_R}
{V_{cc}}\sin (x+\phi)$
Where
$$q=\frac{1}{\omega\sqrt{LC}}$$
With the ...
- 1
0
votes
1
answer
87
views
DSolve returns unevaluated(I need a closed or numerical solution for this system and plot solution)
I am trying to find a solution to this system of differential equations but the program gives the same output without any messages. I would like help. Please find the Mathematica code posted here. a ...
2
votes
1
answer
2k
views
Solving coupled PDE and ODE
I want to solve a system of partial differential equation in Mathematica.
equation is:
$ y_0 = 0.5, t_0 = 30, λ_{12} = 0.3, λ_{13} = λ_{23} = 0.01, λ_{21} = 2.8 $
I am new in Mathematica. Please help ...
- 21
14
votes
1
answer
967
views
Solving optimal control problem when input is constrained
Given a linear time-invariant system:
$$x'(t)=Ax(t)+Bu(t)$$
with initial state $x(0)=x0$ and final state $x(T)=xT$.
The performance measure to be minimized is:
$$∫_0^Tu(t)^2dt$$
The most important ...
- 141
5
votes
1
answer
505
views
Optimizing a parameter in an ODE
I've solved a system of two ODEs using NDSolve which look like this
$\qquad y''-ky'=c, \quad y(t=0)=y_0, \quad y'(t=0)=\sin(a)$
$\qquad x''-kx'=0, \quad x(t=0)=x_0, \quad x'(t=0)=\cos(a)$
Where $c,q,k,...
- 167
0
votes
0
answers
62
views
Converting FindRoot minimization to NMinimze
I have the following orbital insertion simulation that uses a linear-tangent steering law and the FindRoot function to find the parameters $\theta_{0}$ and $\theta_{...
- 1,577
3
votes
1
answer
497
views
Runge-Kutta to find maximum of system of ODEs
I'm trying to understand a code for finding the minimum and maximum for a system of ODEs. Here is the code:
...
- 133