Questions on the use of numerical functions NIntegrate and NDSolve.
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 ...
5
votes
1answer
147 views
Differential Equations with Matrices
I'm trying to implement the differential equation of a Cellular Neural Network in Mathematica as seen below:
...
0
votes
1answer
155 views
NDSolve event handler Question [closed]
I'm trying to plot a ball falling, hitting the ground and coming back up.
without air friction, the equations for the system would be
...
1
vote
1answer
97 views
What do these error messages mean when numerically solving differential equations?
I am using Mathematica to numercially solve the following equations:
...
4
votes
1answer
172 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 ...
0
votes
1answer
76 views
What is the correct way to use NIntegrate inside the FindMinimum function?
I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
0
votes
0answers
70 views
Which integration strategy to use for this product of polynomials?
What would be the ideal integration strategy for a function like this: $$f(x_1,x_2,\dots,x_N)=\prod_{i=1}^Nx_i^{c_i}\Theta(x_i-p_i)$$ where $x_i,p_i\in \mathbb{R}$, $\Theta$ is the Heaviside function ...
4
votes
2answers
511 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 ...
3
votes
0answers
113 views
Principal Value Integration with NIntegrate [closed]
While trying to integrate numerically a function involving singularity (triple pole) I encounter some strange behaviour of Mathematica (I'm using Method -> "PrincipalValue"). Maybe someone can explain ...
6
votes
2answers
137 views
2
votes
1answer
202 views
Calculating volume [closed]
I'm new in mathematica and I'm stucked on how I can get the volume of a solid created by the inequation:
...
2
votes
1answer
47 views
Numerical integration with OwnValues
Say I have a symbol with an OwnValue
a = y
And we define an integration like this
...
4
votes
1answer
90 views
Integrating a list of functions
For the purpose of this minimal example, let's say we have a list of functions, like this:
f[y_?NumericQ] := {NIntegrate[z*y, {z, 0, 1}], a y}
I want to ...
1
vote
1answer
75 views
Syntax for integrating over limits specified by a Table
I wish to use NIntegrate to compute multidimensional integrals. However, I don't want to manually input the limits for the dimensions. I want to store the ...
0
votes
0answers
68 views
FindFit and NIntegrate with dependency between integration variables
I am trying to use FindFit and NIntegrate in this situation:
...
0
votes
1answer
119 views
Integrate on a logarithmic grid
I am trying to solve numerically an integral equation, and from a couple of tests I can see that the result has a strong logarithmic divergence. For my specific problem it is very important to have ...
0
votes
0answers
124 views
How to integrate a multivariate normal in Mathematica? [closed]
I am trying to use Mathematica to integrate this w.r.t $x$, $x$ is 2-dimension.
It looks like this,
$\sum\limits_{i=1}^{20}{\exp \left\{ -\frac{1}{2\sigma _{i}^{2}}{{\left( x-\mu_i ...
0
votes
1answer
53 views
5
votes
1answer
294 views
How to solve a non-linear integral equation?
I have a non-linear integral equation that I'd like to solve with Mathematica:
Solve[Integrate[B[x] v / (B[x] + B[v])^2, {x, 0, 1}] == 1, B[v], {v}]
This ...
0
votes
0answers
109 views
dealing with discontinuity at integration
My problem is about the solution of $2$ non-linear equations which have a single parameter. To be more precise, For given two densities; for example:
...
5
votes
1answer
97 views
Proper use of arbitrary number of variables
So, I'm working on a project where the number of independent variables is not fixed.
Consider a problem of $N$ independent variables, $\boldsymbol{r}$.
I want to perform different things with them. ...
-1
votes
1answer
55 views
FindFit and Integration errors
First off, appologies for what may sound like a newbie question, as I am very new to using Mathematica.
I am trying to find a way to get Mathematica to give me an expression that would describe the ...
9
votes
1answer
637 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 ...
4
votes
1answer
99 views
How to find derivative of a numerical solution, where precision is ambiguous?
I am trying to take the derivative of a numerical solution. I am concerned that the way I'm doing this may be problematic due to numerical error; I think there must be a better way but I'm not very ...
0
votes
0answers
85 views
Issue with WorkingPrecision
I am having the following issue.
I am evaluating a numerical integral, and I need high precision to get good values of the function being integrated.
...
8
votes
4answers
223 views
Numerical integration of a numeric data available as a nested list
I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am ...
2
votes
1answer
99 views
Differences between ParametricPlot3D and NIntegrate
I have a function $f : \mathbb{R} \rightarrow \mathbb{R}^3$ defined in a rather nasty way in mathematica however it's a smooth function and what not. I am interested in $f'[t]$ and when I run it ...
0
votes
0answers
72 views
NIntegrate, view integration options [duplicate]
The Mathematica manual says:
NIntegrate symbolically analyzes its input to transform oscillatory and other integrands, subdivide piecewise functions, and select ...
0
votes
1answer
142 views
Nested Nintegrate - two variable limits of integral
This is, so to say, the next part of the question: Nested NIntegrate - NIntegrate::inum: - error
Now I define three functions:
...
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
110 views
Nested NIntegrate - NIntegrate::inum: - error
I have the problem quite similar as in:
Nested NIntegrate
I define two functions:
...
0
votes
1answer
145 views
NIntegrate Error-Estimate Question
When I do some complicated 4-dimensional integral numerically, Mathematica tells me its estimate for the value of the integral, and its estimate for the value of the error in the calculation.
The ...
2
votes
1answer
149 views
Directional derivative of SiegelTheta
I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
0
votes
1answer
169 views
Problem with NIntegrate in NonlinearModelFit
We are receiving many error messages when using NIntegrate with NonlinearModelFit. Here is a much-simplified version of the code. It arrives at the correct answer after several messages saying that it ...
1
vote
1answer
71 views
Get unique values for integration limits
For an multidimensional integration I want to build up the integration limits with the following code. (the length of vars is also variable)
...
0
votes
1answer
89 views
0
votes
1answer
65 views
How to change variable that has been defined in PDE?
I have a PDE function that contains a variable (named ka). I want to plot the result of my PDE in 1 plot using several different ka values. However, I'm not sure about how to write down this equation. ...
1
vote
0answers
294 views
Speed up Numerical Integration
EDIT:
I need to evaluate a very complicated multi-dimensional Integral. The dimension of the Integral depends on a variable j. Let's make my point clear with the ...
0
votes
0answers
41 views
Contour integration [duplicate]
Possible Duplicate:
Symbolic integration in the complex plane
Does mathematica do Contour integration ? like this one :
$\displaystyle \oint_{\gamma} f(z)\ \mathrm{d}z $
if yes, how ...
7
votes
3answers
312 views
How to integrate functions of linearly interpolated data?
At first, consider integration of pure InterpolatingFunction.
Importing some data (works in v.9, for earlier versions one can use this link to download zipped ...
1
vote
1answer
117 views
How can I handle curve singularity in this NIntegrate integration?
Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region.
(Why ...
1
vote
1answer
219 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:
...
3
votes
1answer
252 views
Efficient way to perform elementary integration step with NDSolve internal method
I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via Method option).
Such a possibility is crucial for me, since ...
4
votes
1answer
206 views
Using a compiled function inside NIntegrate gives “CompiledFunction::cfsa” message
The following function is defined for Real input:
FFc = Compile[{{x, _Real}, {EF, _Real}},If[x > EF, 0., If[x == EF, 0.5, 1.]]]
FFc is now used in the ...
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
...
9
votes
1answer
466 views
I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve
@DNA
The fluid here has been assumed as single component perfect gas i.e. it obeys the equation P=ρRT, the thermal conductivity is assumed as a constant, so the equation is:
...
2
votes
2answers
167 views
Making NIntegrate behave like a listable function
I have a function defined by
$$f(t)=\int\limits_0^t g(x) dx$$
$g(x)$ is a complicated function (specifically the Mittag-Leffler function which has recently been implemented in Mathematica 9 as ...
