Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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1answer
258 views

Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
-6
votes
1answer
184 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
1
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2answers
247 views

How to numerically integrate this integral?

I want to integrate a function (spherical coordinates): $$\int _0^{2 \pi }\int _0^{\pi }\frac{r^2 \sin (\theta ) e^{-\lambda \sqrt{\rho ^2+r^2-2 \rho r \cos (\theta )}-2 r}}{\pi \epsilon ...
1
vote
1answer
234 views

Integrate with FunctionInterpolation differs from NIntegrate

In working with interpolating functions and integration, I noticed a lot of differences between NIntegrate and Integrate in the ...
1
vote
2answers
341 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
3
votes
0answers
158 views

Non-linear integral equation

I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be ...
2
votes
1answer
200 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
12
votes
3answers
1k views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
0
votes
0answers
87 views

Speeding up Integrate and the numerical solution

I want to compute the drag of a plate Below is the code I am using to integrate the function ...
0
votes
1answer
279 views

Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
4
votes
2answers
312 views

How to use NIntegrate when there are symbolic constant coefficients

I would like to numerically integrate an equation such as the one below in which there are symbolic constant coefficients. I used a very simple code but it doesn't work in general, that tried to deal ...
0
votes
0answers
54 views

MathLink wrapper for NIntegrate

I wonder if I can benefit from the Mathematica numerical quadrature routines in a way which integrates completely into an existing C-program. To be more specific I have C-program which does numerical ...
0
votes
3answers
337 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
0
votes
0answers
114 views

Can this function be numerically integrated

I need to integrate the function, $f(a,b)=-g(a,b)ln(g(a,b)) = -1/ Pi(( (E^(-((a^2 - E^(-t [Gamma]) [Alpha]^2)/( 1 + 2 [Sigma]^2)))) [Pi] ([Sigma]^2) )/((1 + 2 [Sigma]^2) (E^(2 ...
-1
votes
1answer
291 views

Multiple NIntegrate (again)

Basically I have the same question as here: Multiple NIntegrate but since I don't have enough "reputation" I cannot comment there. I want to solve the following multiple Integral numerically at given ...
0
votes
1answer
345 views

Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
3
votes
1answer
250 views

Integrate equations of motion when force depends on position

I'm fairly new to Mathematica. I'm trying to test my C++ implementation of a fourth order Runge Kutta method for Newton's equations of motion. I want to test my integrator when the applied force is ...
1
vote
1answer
288 views

Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
0
votes
2answers
515 views

Double integral with variable in the limits

I'm trying to solve this integral: $$ ...
2
votes
1answer
416 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 ...
5
votes
1answer
982 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
0
votes
0answers
229 views

Using Mathematica to Solve for Electric Field from finite cylinder

For a cylinder that is of length L and radius s and possesses a charge distribution of sigma across only the cylinder part and not the endcaps, I am trying to calculate the Electric-field. The ...
1
vote
2answers
180 views

How to make a single-variable out of a NDSolve solution?

So I've got this line that contains the solution of a partial, non-extraordinary differential equation (because Mathematica doesn't handle extraordinary partial differential equations): ...
2
votes
1answer
535 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
0answers
174 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 ...
1
vote
0answers
196 views

Choosing PrecissionGoal and AccuracyGoal for decomposed integral with NIntegrate

Assume I have a complicated integral $I$ which can feature all kinds of difficulties like infinite interval, rapidly oscillatory integrand, integrable singularities and numerically almost singular ...
1
vote
3answers
1k views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
8
votes
1answer
309 views

Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
9
votes
2answers
393 views

Why do I get a different value when I change the order of integration?

I think the following two-dimensional integrals should be equal, since they both integrate the function over the half plane defined by $t>\tau$. $$\int_{-\infty}^\infty \mathrm{d}t ...
5
votes
5answers
751 views

NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to ...
4
votes
1answer
290 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
3
votes
1answer
365 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
0
votes
1answer
489 views

How to use NIntegrate in a function using parameters from a list

I would like to use NIntegrate in a function with some parameters from a list. I simplified my problem for this forum. The list of parameters is as follows: ...
0
votes
0answers
125 views

ParametricNDSolve: Parameter inside UnitStep leads to longer integration times

I have found one of the most annoying issues in ParametricNDSolve. When a parameters occurs inside UnitStep (and Piecewise and If) the integration takes much longer time. I illustrate this by an easy ...
3
votes
1answer
514 views

Question on accuracy and precision of NIntegrate

As a Mathematica newbie, I was testing the accuracy/precision of NIntegrate (9.0.1.0 on Mac) and have obtained a very peculiar result. ...
0
votes
0answers
76 views

PDE syntax question

I am trying to solve a PDE of a reaction diffusion equation, and while I'm getting a decent looking solution, I am also getting inconsistent BC / initial conditions warnings and wanted to check if my ...
0
votes
0answers
187 views

Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$ dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X $$ where X is a random variable (e.g. from a ...
0
votes
2answers
249 views

NDSolve boundary query / Extracting values from solution

I have a function $O_{2}$ with boundary conditions $O_{2}(r_{o}) = p_{o} $ and $O_{2}(g) = O_{2}'(g) = 0$. I plot it using the solver code below; ...
2
votes
0answers
176 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
5
votes
2answers
235 views

Triple fractional part-related integral

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
14
votes
1answer
254 views

Inconsistent behavior of WhenEvent[ ]

Consider the following simple example: ...
1
vote
2answers
765 views

Kramers Kronig Relation for Phase and Complex Reflectivity

I am a new user to Mathematica and I have been trying to figure out how to find $\Theta(\omega)$ from my 'experimental' values of energy and $\ln(\sqrt{R(\omega)})$ (I am just running a simulation, ...
1
vote
1answer
1k views

shooting method and stifness problem for NDSolve

I'm trying to solve numerically the following differential equation: 1/r[x]^5 + k/Sqrt[1 + r'[x]^2] - (k r[x]r''[x])/(1 + r'[x]^2)^(3/2) == 0 I can set boundary ...
0
votes
0answers
174 views

NIntegrate with an arbitrary number of variables [duplicate]

I need to evaluate NIntegrate with a variable number of variables. Here's a concrete example. I'll accept an answer that finds a way to make the example work. I ...
10
votes
3answers
807 views

Different results for integration using Mathematica and MATLAB

I have the following integration: $$\text{y}=2 \sqrt{\frac{1}{\pi }} \int_0^{\infty } \frac{e^{-z} \left(1-e^{-\frac{z}{b}} \left(\frac{a}{a+c z}\right)^L\right)}{\sqrt{z}} \, dz$$ I get different ...
0
votes
2answers
194 views

NIntegrate using Boole doesn't work

This doesn't want to work for me - I don't know why not. It usually gives me 0, but sometimes also a different number. I know it should be a small, non-zero number. ...
2
votes
1answer
124 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
0
votes
0answers
66 views

How to solve initial value problem using Runge-Kutta method? [duplicate]

How to solve the following initial value problem using Runge-Kutta method u''[x] + (2/x) u'[x] + E^(u[x]) == 0, u[0] == 0, u'[0] == 0
1
vote
1answer
236 views

Interpolation of a table with 4 parameters

I have a huge data file which I need to do some analysis on it. The file is built in this way that for each 4 variables, there is a value of the function: ...
2
votes
1answer
418 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: ...