Questions on the use of numerical functions NIntegrate and NDSolve.
3
votes
0answers
114 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 ...
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
2answers
516 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 ...
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
69 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 ...
6
votes
2answers
137 views
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," ...
0
votes
1answer
53 views
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
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
300 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 ...
-1
votes
1answer
56 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 ...
4
votes
1answer
101 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
86 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.
...
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 ...
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 ...
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. ...
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 ...
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
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:
...
0
votes
1answer
111 views
Nested NIntegrate - NIntegrate::inum: - error
I have the problem quite similar as in:
Nested NIntegrate
I define two functions:
...
0
votes
1answer
146 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 ...
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
90 views
0
votes
1answer
66 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. ...
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
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 ...
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 ...
7
votes
3answers
316 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
0answers
295 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 ...
1
vote
1answer
220 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 ...
2
votes
1answer
205 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:
...
5
votes
1answer
111 views
How can I deal with an NDSolve::ivone message regarding boundary values?
I have a question regarding the error message:
...
4
votes
1answer
208 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
1answer
171 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 ...
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
154 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
...
2
votes
2answers
168 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 ...
0
votes
0answers
187 views
Mathematica 9's NDSolve treats sum as an integral [closed]
Sum and integral are threated the same by NDSolve in Mathematica 9:
The problem was also in Mathematica 7. I submitted a bugreport to the technical support, they admitted this is a bug, fixed it in ...
2
votes
2answers
188 views
Problem with setting working precision in NIntegrate
I want to obtain a good numerical approximation (up to 10 decimal place would be ok for me) to an integral:
$$
\int^{\infty}_{0} f(r)r^2dr
$$
I am using the function $f(r)$, which is related to the ...
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 ...
2
votes
0answers
139 views
FindRoot - Speed and errors
I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
votes
1answer
139 views
Singular integral: NIntegrate fails to converge
I need to calculate the following singular integral:
NIntegrate[Log[1 + y^2]/Cos[Pi y], {y, 0, 1}]
However, it is failing to converge. I have tried to specify ...
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 ...
0
votes
1answer
143 views
Nested NIntegrate problem
So I've been trying to evaluate the following integral in Mathematica 8.0 Student version:
...
4
votes
1answer
177 views
Integral of integral — it takes too much time
When I evaluate the following expression in Mathematica, it takes so much time that I don't want to wait for the evaluation to complete. So I think that there must be a better approach.
...
