Questions on the use of numerical functions NIntegrate and NDSolve.

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4
votes
2answers
577 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 ...
15
votes
6answers
2k 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? ...
0
votes
1answer
508 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 ...
2
votes
1answer
462 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 ...
2
votes
1answer
1k views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
1
vote
1answer
383 views

What do these error messages mean when numerically solving differential equations?

I am using Mathematica to numercially solve the following equations: ...
6
votes
1answer
807 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
3
votes
1answer
2k 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 ...
2
votes
1answer
90 views

Numerical integration with OwnValues

Say I have a symbol with an OwnValue a = y And we define an integration like this ...
14
votes
3answers
6k views

Solving a time-dependent Schrödinger equation

I want to solve the time-dependent Schrödinger 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 that ...
5
votes
2answers
291 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 ...
2
votes
1answer
354 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
1answer
636 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
338 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
0
votes
1answer
569 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
102 views

Error with minimization of NProbability

I'm trying to solve the following problem: ...
19
votes
1answer
4k views

How to solve a non-linear integral equation?

I have a non-linear integral equation that I'd like to solve with Mathematica: $$ \int_{0}^{1} \mathrm{d}x \frac{B(x) v}{(B(x) + B(v))^2} = 1$$ ...
-1
votes
1answer
125 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
260 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 ...
2
votes
1answer
155 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 ...
9
votes
4answers
1k 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 post-...
5
votes
1answer
521 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
89 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
2k 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
1k views

Nested NIntegrate - NIntegrate::inum: - error

I have the problem quite similar as in: Nested NIntegrate I define two functions: ...
0
votes
1answer
668 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
400 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
91 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
137 views

Differential Equation help

I have a differential equation that looks like this: ...
0
votes
1answer
150 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. ...
4
votes
1answer
473 views

Differential Equations with Matrices

I'm trying to implement the differential equation of a Cellular Neural Network in Mathematica as seen below: ...
2
votes
1answer
541 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 ...
22
votes
4answers
2k 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
1k 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
797 views
2
votes
1answer
381 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
1k views

How can I deal with an NDSolve::ivone message regarding boundary values?

I have a question regarding the error message: ...
17
votes
2answers
1k views

Using a compiled function inside NIntegrate gives “CompiledFunction::cfsa” message

The following function is defined for Real input: ...
3
votes
1answer
912 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
557 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
954 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 ...
3
votes
2answers
1k 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 ...
8
votes
2answers
517 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 one....
2
votes
0answers
407 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 ...
3
votes
1answer
935 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 <...
5
votes
1answer
367 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
559 views

Nested NIntegrate problem

So I've been trying to evaluate the following integral in Mathematica 8.0 Student version: ...
4
votes
1answer
275 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. ...
2
votes
1answer
809 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 ...
0
votes
2answers
284 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 ...