Tagged Questions
2
votes
2answers
63 views
3
votes
0answers
61 views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
...
2
votes
1answer
51 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
6
votes
2answers
157 views
How to deal with zero in NDSolve in mathematica?
I would like to solve the following ODEs
$$\begin{cases} x'(t)&=y\\
y'(t)&=-y(t)/t-e^{x(t)},\\
x(0)&=1,\\y(0)&=0,
\end{cases}$$
(EDIT :
The second equation used to be $y'(t) = ...
1
vote
0answers
84 views
NDSolve diffusion equation over/underdetermined
I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak.
I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
0
votes
1answer
102 views
DAE - varying initial conditions
I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here:
Putting NDSolve into ParametricPlot
But it does not work:
...
16
votes
2answers
351 views
3D orbits and inaccuracy over time
I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
1
vote
1answer
86 views
How to adjust parameters to experimental data on a NDSolve problem
I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3.
...
7
votes
0answers
128 views
Numerically solve 2nd order differential equation with singularity
Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example:
$$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$
where ...
6
votes
1answer
58 views
1
vote
1answer
134 views
How to plot and solve the numerical solution of a integro-differential equation
I have a integro-differential equation of the form
$y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$
My code is:
...
0
votes
1answer
63 views
Notation for numerical solutions to differential equations
Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation:
...
1
vote
0answers
111 views
Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
2
votes
1answer
64 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
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3
votes
1answer
55 views
How to integrate ParametricNDSolve solution with respect to a parameter?
I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
4
votes
1answer
158 views
NDSolve for a large system of simple ODEs
I am solving a system of many (more than 100) ODEs.
It is the kind of standard rate equation encountered in semiconductor physics.
Here is the system:
...
4
votes
1answer
58 views
Differentiating ParametricNDSolve solutions
Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
1
vote
2answers
91 views
NDSolve solution for driven damped pendulum diverges
I want to solve numerically for the system of the driven damped pendulum using Mathematica. This is the second-order nonlinear equation
\begin{equation}
\ddot{x} + 2 \beta \dot{x}+ \omega_0^2 \sin
...
2
votes
2answers
162 views
Animating the Lorenz Equations
I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck.
The equations are:
...
1
vote
1answer
99 views
How does one specify Neumann conditions for NDSolve?
I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works:
...
1
vote
1answer
132 views
Problems with NDSolve and stiffness
I am trying to solve an ODE in chemical kinetics:
$$\begin{align*}
\frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\
\frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y]
\end{align*}$$
My ...
13
votes
1answer
260 views
Optimizing a Numerical Laplace Equation Solver
Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
1
vote
2answers
341 views
Solving a system of ODEs with the Runge-Kutta method
I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the ...
3
votes
2answers
134 views
How to remove a singularity with WhenEvent
Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
0
votes
0answers
81 views
NDSolve divergence in Mathematica 9
I have been working with Mathematica 7 and 8 to numerically solve partial differential equations by MethodOfLines of NDSolve. ...
4
votes
2answers
123 views
3
votes
2answers
105 views
Putting NDSolve into ParametricPlot
I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values.
I have a code that has several stages, which seem to ...
6
votes
0answers
63 views
Modify NDSolve`StateData (if possible)
I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData.
Now, the problem is, I'm not used to ...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
2
votes
2answers
101 views
BC for transport equation using NDSolve
First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
4
votes
1answer
169 views
NDSolve does not respond
For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
4
votes
2answers
506 views
Solving a time-dependent Schroedinger equation
I want to solve the time-dependent Schroedinger equation:
$$
i\partial_t \psi(t) = H(t)\psi(t)
$$
for matrix, time-dependent $H(t)$ and vector $\psi$.
What is an efficient way of doing this so ...
0
votes
1answer
144 views
Applying l'Hôpital's Rule to NDSolve with Piecewise Function
OK, so I've been working on this problem for over a week and it's driving me crazy.
I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
1
vote
0answers
121 views
NDSolve equations contain solution from solving cubic equations
I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations.
In my problem, I first obtained 6 functions (ca1, ...
0
votes
1answer
89 views
1
vote
1answer
100 views
Using NDSolve solution as initial condition for another NDSolve
I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
5
votes
1answer
109 views
How can I deal with an NDSolve::ivone message regarding boundary values?
I have a question regarding the error message:
...
0
votes
0answers
125 views
Numerical solution of a system of ODEs
I have to solve set of coupled first order ODE's
$y_1=z$, $ y_2=\frac{dz}{dt} $;
$\frac{d^2y_1}{dt^2}=\frac{dy_2}{dt}=\frac{(p_s-p_f)}{p_s}g-\frac{9u}{2a^2p_s}y_2 $
Using the Euler method and the ...
1
vote
1answer
153 views
NDSolve for PDE with discontinuous initial/terminal condition
I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution
...
6
votes
2answers
151 views
Catching only the first event in NDSolve EventLocator
I have a system of ODEs that I solve. During the integration process, there's an event that I want to catch, but I want to (a) continue the integration after the event and (b) catch only the first ...
6
votes
1answer
210 views
NDSolve and WhenEvent Causing Excess Work
When I use the following system
model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5}
with the ...
2
votes
1answer
208 views
Differential equations with jump conditions
Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
1
vote
2answers
156 views
System of ODEs specified by large coefficient matrices
What is the best way to call NDSolve for solving a system of differential equations of the form
...
2
votes
0answers
190 views
Inconsistent boundary and initial conditions: BC ignored altogether
Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary:
...
3
votes
1answer
470 views
NDSolve with vectors
I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
4
votes
1answer
379 views
Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?
I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs:
...
1
vote
1answer
177 views
How to solve a system of ordinary differential equations contain a interpolating function?
I'm wondering how I can solve a system of ODE that has a interpolating function? For example, z and y are ...
9
votes
1answer
636 views
Numerically solving an inhomogeneous partial differential equation
I'm trying to solve a cylindrical partial differential equation with boundary conditions. But I got an error message saying ...
1
vote
0answers
109 views
NDSolve Convergence test failure and significant effect of DifferenceOrder on eventual results
I am solving a non linear partial differential equation with what I call free boundary conditions (solid mechanicists would know this as simply supported).
I realized that this boundary condition ...
7
votes
1answer
142 views
The only usage for the option InterpolationOrder in NDSolve is to be set to All?
We know that changing the option InterpolationOrder in ListLinePlot、ListPlot3D、...
