Questions on the use of numerical functions NIntegrate and NDSolve.

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3answers
2k views

Retrieve values of InterpolatingFunction

While analyzing a large system of ODE's, I defined a particular ratio p, which contains some variables that are represented by ...
2
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2answers
117 views

NIntegrate - WorkingPrecision

I am trying to NIntegrate this expression. It is very close to zero, and so gives all possible types of errors. More precisely, ...
2
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1answer
162 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
2
votes
2answers
198 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
2
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1answer
351 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
2
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1answer
419 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?
2
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2answers
774 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 ...
2
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1answer
550 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 ...
2
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1answer
187 views

tricky memoization

Let's say I have the NDSolve example for documentation involving splitting 2nd order into set of 1st order ODEs: ...
2
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1answer
43 views

Imaginary term in Integration procedure

How do you remove the imaginary term in the integrated output? Compare the outcome from the operations below. The first operation yields an imaginary term, while the second one has none. ...
2
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1answer
212 views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
2
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1answer
410 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
2
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2answers
411 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 ...
2
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1answer
78 views

Numerical integration with OwnValues

Say I have a symbol with an OwnValue a = y And we define an integration like this ...
2
votes
2answers
494 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 ...
2
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1answer
237 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 ...
2
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1answer
674 views

Solving a PDE containing DiracDelta

I want to get the answer from a PDE: $$\begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
2
votes
1answer
517 views

How to use NDSolve to track a deviation from equilibrium?

i have a task to find a event, to achieve this i think need to integrate until a constant function suddenly breaks the equilibrium and give a sharp peak. I think that EventLocator should work, thus ...
2
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1answer
90 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
2
votes
1answer
117 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} ...
2
votes
2answers
114 views

What is the proper way to operate on interpolating functions?

I am trying to multiply an interpolating function by -1. If I do this Mathematica does not seem to allow any further operations. Bear with me while I generate the Interpolating Function in question. ...
2
votes
1answer
554 views

Obtain a stable solution using NDSolve

I am trying to solve a partial differential equation using NDSolve. When I am not specifying any method options with NDSolve, it ...
2
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2answers
302 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
2
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1answer
134 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 ...
2
votes
1answer
290 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 ...
2
votes
2answers
613 views

Problem with NDsolve for a system of equations

I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!! Please have a look at the problem and result and help me with your ...
2
votes
2answers
153 views

How can i integrate over a set of data

i need to integrate over my data, which is denoted as {q, I},here I is the Intensity i need to obtain the form of the following integration( its not a numeric integration, because it contain x, next ...
2
votes
1answer
158 views

Numerical Integration with Variable Parameters

So I want to numerically compute the integral of a long complicated expression over a specified domain (in this case an ellipse). I know how to use a Boole function to sample within the ellipse, but I ...
2
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1answer
80 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
2
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1answer
260 views
2
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2answers
114 views

Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
2
votes
1answer
425 views

Differential equations: Solving a singular/nonlinear ODE using NDSolve

I am trying to numerically solve a rather horrible looking singular/nonlinear ode: A*(y''[x]/y[x])'' +y[x]^2==1 on the interval ...
2
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1answer
262 views

Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
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2answers
536 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 ...
2
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1answer
151 views
2
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1answer
86 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
2
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1answer
173 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
2
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1answer
213 views

How to use NIntegrate in a purely numerical mode?

I have a function that is defined as the smallest root of a given polynomial. Something like this: ...
2
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1answer
150 views

Plotting Laplace's equation on an infinite domain

I am trying to plot my solution to a Laplace equation on an infinite domain. However, when I try to plot it, Mathematica just runs with nothing happening. ...
2
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1answer
309 views

Avoiding zero (empty set) solution with NDSolve

I'm trying to use NDSolve for a chemical kinetics equation where the rate of conversion is given by this relationship as typed in Mathematica: ...
2
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1answer
269 views

Numerical integration involving Inverse Normal CDF

I'd like to evaluate the following numerical integration using Mathematica $$ \ \int_0^T\int_0^\infty xe^{-0.04 s}g(x,s) dxds\ $$ where g(x,s) is a Gaussian copula function with say, marginal ...
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1answer
432 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 ...
2
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1answer
384 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. ...
2
votes
1answer
215 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 ...
2
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1answer
240 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
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1answer
212 views

how to nest parallelized computations on a cluster?

I am lucky to have access to a computational cluster and I could submit my job to many-many cores. As I need to evaluate a numerical integral within a numerical integral, I would like to know if I can ...
2
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0answers
42 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: ...
2
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0answers
121 views

Global vs local adaptive integration: lattice propagator

I was doing the first exercise in the paper Lattice QCD for Novices. This is the expected result: With the default "GlobalAdaptive" method for NIntegrate it threw errors saying that the error had ...
2
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0answers
108 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
2
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0answers
90 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...