Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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1answer
46 views

Strange result using NIntegrate with Max and PDF

This is really trivial and I appologise in advance if I have made a stupid error somewhere. I have been chasing down some strange results when using NIntegrate with ...
2
votes
1answer
102 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
1
vote
1answer
200 views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
0
votes
1answer
40 views

NDSolve with arrays and Tables of Equations and WhenEvent

I've been toying around with NDSolve for a while, and read through the website. By doing so I discovered that I could use it for vectors and arrays with much pleasure. So I wanted to write a simple ...
0
votes
1answer
86 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, ...
-5
votes
1answer
83 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
0
votes
2answers
248 views

Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: $$\begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*}$$ My ...
1
vote
1answer
52 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 ...
0
votes
2answers
88 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
10
votes
3answers
601 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 ...
1
vote
1answer
157 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: ...
1
vote
2answers
90 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: ...
1
vote
1answer
237 views

Simpson's rule with ListConvolve or ListCorrelate

I have a function that's represented as a long list of values that I want to integrate. I can do it procedurally with Simpson's rule. ListConvolve generally runs faster then procedural code, so i ...
3
votes
0answers
79 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 ...
1
vote
1answer
99 views

ParametricNDSolve: Fails to differentiate an matrix differential equation

It seems like there is a problem with differentiating a ParametricNDSolve object when the underlying system contains an matrix differential equation. Create a simple ParametricNDSolveValue object ...
4
votes
2answers
158 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
59 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
0answers
32 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
0answers
66 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
vote
1answer
157 views

Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
3
votes
1answer
131 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. ...
4
votes
1answer
350 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 ...
-1
votes
1answer
85 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 ...
3
votes
1answer
140 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
84 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
108 views

Double integral with variable in the limits

I'm trying to solve this integral: $$ ...
1
vote
2answers
109 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
61 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 ...
0
votes
0answers
95 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 ...
0
votes
1answer
123 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
1
vote
1answer
241 views

Table not working with Plot

Because NIntegrate[] does not support parallel computation out of the box, I'm doing a simplified version by breaking the integration limit into pieces and using ...
2
votes
0answers
88 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
56 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 ...
3
votes
1answer
251 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? ...
1
vote
3answers
154 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; ...
7
votes
2answers
219 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 ...
1
vote
0answers
195 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
0
votes
0answers
63 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
4
votes
1answer
171 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 ...
7
votes
1answer
180 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. ...
0
votes
1answer
84 views

Transformation of the NDSolve result into new dependent variables

I have solved a set of coupled differential equations and now I need to convert them into different dependent variables and sketch their trajectories. Here is the code I have written so far: ...
4
votes
5answers
129 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 ...
0
votes
1answer
74 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
52 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 ...
2
votes
1answer
158 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: ...
0
votes
0answers
43 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 ...
8
votes
4answers
282 views

NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
0
votes
0answers
71 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 ...
2
votes
0answers
69 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
0
votes
2answers
315 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, ...