Questions on the use of numerical functions NIntegrate and NDSolve.
5
votes
0answers
154 views
2
votes
2answers
80 views
2
votes
1answer
52 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
3
votes
0answers
63 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:
...
6
votes
2answers
159 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) = ...
2
votes
0answers
78 views
Solving homogeneous Fredholm Equation of the second kind
I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e.
$\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$
where $\lambda$ is the eigenvalue (to be ...
1
vote
0answers
82 views
Getting MemoryAllocationFailure from NIntegrate
When numerically calculating a double integral using NIntegrate over an infinite domain (with all options at their default), Mathematica 7 calculates my integral ...
0
votes
1answer
107 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:
...
1
vote
0answers
85 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 ...
2
votes
0answers
31 views
NIntegrate/NSum with parameters [duplicate]
I'm trying to calculate a continuous integral within a discrete integral.
Something similar to this (yet more complex):
...
16
votes
2answers
353 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
87 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.
...
10
votes
1answer
213 views
Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?
I am trying to evaluate this integral numerically
$$
\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q
$$
for large values of $R$. This makes the integrand oscillate more quickly and Mathematica ...
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
60 views
2
votes
0answers
152 views
Is mathematica storing information it shouldn't store?
I'm seeking to find solutions to a numerical integration with a large set of parameter combinations (basically, I'm doing a brute parameter sampling). Yet, I believe the memory of the computer is ...
4
votes
1answer
159 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
0answers
59 views
Very long evaluation time of NDSolve [closed]
The following code takes a very long time, and I am not quite sure why. The Quiet is needed as otherwise there are many error messages of the form ...
1
vote
1answer
135 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:
...
1
vote
0answers
113 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 ...
8
votes
1answer
338 views
1D Euler Equations
Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve?
For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm
Using ...
0
votes
1answer
64 views
Notation for numerical solutions to differential equations
Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation:
...
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:
...
8
votes
2answers
132 views
Problem with NIntegrate when WorkingPrecision is specified
I am trying to evaluate this integral numerically:
$$
\int_0^{\infty } m \exp (-m) J_1(m){}^2 \, dm
$$
Everything is OK when only the integration method is specified:
...
2
votes
1answer
64 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
...
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
59 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
...
8
votes
5answers
253 views
How do I obtain the enclosed area of this particular parametric plot?
I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how?
...
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:
...
13
votes
1answer
261 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 ...
3
votes
3answers
145 views
How to speed up the plot of NIntegrate?
Here is a toy example:
f[t_] := NIntegrate[Sin[x], {x, 0, t}];
Plot[f[t], {t, 0, 10}] // Timing
Even such a simple example will take 2.8 seconds on my computer.
...
0
votes
1answer
66 views
Error messages when using NInverseFourierTransform
I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
3
votes
2answers
135 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 ...
1
vote
1answer
133 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 ...
6
votes
3answers
359 views
Strategies to solve an oscillatory integrand only known numerically
I have an integrand that looks like this:
the details of computation are complicated but I only know the integrand numerically (I use NDSolve to solve second ...
0
votes
1answer
75 views
NIntegrate fails while Integrate works
I have a function $f(t)$ defined as
$f(t)=\int\limits_0^t(t-\xi)^{\alpha-1}\ \cos(\xi)\ d\xi$
where $0<\alpha<1$. I now want to evaluate this integral at various values of time. Therefore, my ...
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 ...
1
vote
2answers
344 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 ...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
1
vote
0answers
130 views
How can I speed up numerical integration of multidimensional integral?
I am numerically solving an integral equation that contains a double integral. I have managed to get a solution but it takes forever. I am wondering if there is a way to speed up numerical integration ...
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," ...
2
votes
1answer
214 views
Creating hexahedral finite elements in Mathematica
Is it possible to do FEM using hexahedral elements in Mathematica? If it possible, is there any help to do that?
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
14
votes
1answer
214 views
Why does LogLinearPlot sample its argument outside the specified domain?
I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this,
...
-1
votes
1answer
119 views
double integration
I want to evaluate a double integral, but the limits of one integral is a function of the second. Like this
...
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 ...
