Questions on the use of numerical functions NIntegrate and NDSolve.

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3
votes
0answers
54 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
1
vote
0answers
55 views

Problems with NIntegrate, levmaxord error

I am trying to integrate some spherical harmonics, for scattering over a sphere, using the SphericalHarmonicY and NIntegrate ...
0
votes
0answers
53 views

Numerical integration with large exponents

To make a long story short, I am doing mostly analytic calculations and therefore do note have good skills in numerical integration. I have to numerical integrate the following integral ...
2
votes
1answer
126 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
2
votes
0answers
48 views

Number recognition in Mathematica [closed]

Suppose that I have a number $n$ with many decimal digits of precision. What is the code to use to get Mathematica to recognize possible closed-form expressions for that number?
0
votes
1answer
79 views

How to compute an integral with 300 digits accuracy [closed]

I'm new to Mathematica and I would like to ask what is the code to use to calculate numerically an integral with 300 digits precision; also, I would like to know what is the right code to use the ...
1
vote
1answer
74 views

Computer freezes during NIntegrate[]

I have a notebook that freezes the computer every time I run it (I mean the whole computer becomes unresponsive and do not react to ctrl-shift-esc and ctr-alt-delete as well as alt-tab and ...
1
vote
0answers
63 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times ...
2
votes
1answer
84 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
1
vote
1answer
76 views

How to evaluate complex numerical integral in mathematica?

I have an integral of the form \begin{align} F(\omega) = \int_0^{\infty} f(s,\omega) \mathrm{d}s \end{align} which I would like to numerically evaluate and plot for a range of $\omega \in ...
1
vote
1answer
120 views

Solving Fredholm Equation of the first kind [duplicate]

I want to numerically solve Fredholm integral equations of the first kind, equations of the form $$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$ where we know the functions $K(t,s)$ and $g(t)$ and seek to ...
0
votes
1answer
81 views

NIntegrate:eincr error

I am trying to solve this expression in Mathematica with the function NIntegrate: ...
0
votes
2answers
75 views

NIntegrate Error

I am trying to solve this expression with the function NIntegrate: ...
3
votes
2answers
101 views

NIntegrate giving message NIntegrate::slwcon:

I got this interesting answer from Mathematica when trying to integrate my function numerically: f[x_] := Sqrt[17*x^2 + x^4] NIntegrate[f[x], {x, -1, 2}] ...
1
vote
1answer
111 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
4answers
176 views
2
votes
0answers
89 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
2
votes
1answer
145 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
0
votes
2answers
92 views

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
2
votes
0answers
116 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: ...
7
votes
2answers
150 views

Efficient way to obtain values of a function defined by an Integral

Consider the following equation: $$S(q)=\frac{(4 \pi \rho ) \int r (h(r)-1) \sin (q r) \, dr}{q}$$ I want to numerically obtain values for $S(q)$ given that I have data points representing $h(r)$ ...
2
votes
1answer
85 views

Calculate the relationship between the duration of two oscillating functions

I am trying to quantitatively determine the relationship between the length of two oscillating functions. Meaning, what is the duration of the green spike in relation to the blue square? Does anyone ...
1
vote
1answer
128 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
0
votes
0answers
82 views

How do I perform the following numerical integration

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
4
votes
1answer
77 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...
4
votes
1answer
127 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...
7
votes
2answers
210 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns several error messages: ...
4
votes
3answers
422 views

Find arc length

I am trying to find the arc length for using ...
5
votes
1answer
107 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
1
vote
2answers
138 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
0
votes
0answers
45 views

Getting message NIntegrate::inumr: in V10; did not happen in V9 [duplicate]

I just tried making a ParametricPlot that worked error-free in Mathematica 9, but now produces errors before successfully plotting in Mathematica 10. It appears to ...
3
votes
0answers
57 views

NIntegrate::ncvbr: How should we interpret and handle this error not mentioned in any documentation?

I have some user-defined module describing my integrand which has to be computed numerically (it's much more complicated than this but bear with me): ...
1
vote
3answers
121 views

Improving convergence in a numerical integration (Version 5.2)

I have a double integral that I am trying to calculate numerically, and I'm having convergence issues. ...
0
votes
0answers
76 views

Problem solving a Fredholm integral equation

Based on the algorithm by PlatoManiac presented here Integral equation numerical solution with NDSolve I am solving a Fredholm integral equation with the following constants and arguments: ...
9
votes
1answer
165 views

Is this a bug in NIntegrate?

Bug is present as of version 10.0.2 checked on windows 7, 64 bit Is this a bug or I missed something? NIntegrate seems to give a different answer for the same ...
4
votes
1answer
113 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
4
votes
2answers
125 views

NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
1
vote
1answer
80 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
-2
votes
2answers
140 views

Use MATHEMATICA to calculate the volume of the solid [duplicate]

Use MATHEMATICA to calculate the volume of the solid that results when the region enclosed by the given curves is revolved about the x- axis. f(x)=Pi^2 Sin[x] Cos[x]^3, f(x)= 4 x^2 x=0, x=Pi/4
4
votes
2answers
238 views

Approximate value for the area between the curve

I've got this task: Use Mathematica to obtain an approximate value for the area between the curve $y=1/4$ and the x-axis over the interval $[1,2]$ with $50$ subintervals using the left ...
0
votes
1answer
114 views

Plotting an function defined by an integral [closed]

How can I plot a function defined by an integral. More specific, I have the following equation: $$ T = ...
1
vote
2answers
648 views

Computing 10-dimensional volume of a 9-sphere [closed]

I'm trying to compute 10-dimensional volume of a 9-sphere with radius r using Monte Carlo. ...
2
votes
1answer
92 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
5
votes
2answers
148 views

Example of Integrate applying a numerical evaluation N

Here is a minimal example: Integrate[(a[1] + x)^2, {x, 1., 2.}] 2.33333 + 3. a[1.] + 1. a[1.]^2 The problem is that ...
7
votes
1answer
140 views

How do I speed up a plotting of NIntegrate when repeated multiple times inside Plot?

I am studying a set of functions (many of which I know only as a definite integral) and I have assembled into a list. Here is a sample: ...
2
votes
1answer
44 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. ...
6
votes
3answers
133 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
0
votes
0answers
48 views

NIntegrate with and without MaxRecursion

Ran a mathematica code using NIntegrate containing an integration over spherical and normal bessel functions. 1.Would the answer in the two cases change if I use MaxRecursion with some number of ...
0
votes
0answers
42 views

Difficult to solve the equation using FindInstance and not able to solve it numerically

I hope to find the range of a which leads to non-zero solution of H when you are given a specific value of B. And I hope to get ...
-1
votes
1answer
473 views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...