Questions on the use of numerical functions NIntegrate and NDSolve.

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1
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4answers
80 views
1
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1answer
55 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
0
votes
2answers
66 views

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
0
votes
0answers
43 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
2
votes
0answers
47 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: ...
0
votes
0answers
24 views

Numerical Integration for Different Values of a Parameter + Making a Table [on hold]

I have the following issue: I have an integral with a known lower and upper bound as a function of a parameter. Let's say my parameter is a, and lower bound is sqrt(a) and upper bound is sqrt(2a). I ...
7
votes
2answers
133 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
0answers
64 views

Solving Laplace's equation in rectangle domain by separation of variables

I wanted to solve numerically Laplace's equation $\Delta \psi = 0$ by separation of variables, ie: 1.) ansatz $\psi(x,y,t) = X(x)Y(y)$ (t will be important later, think of it as a parameter) 2.) ...
1
vote
1answer
84 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
0
votes
0answers
44 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 ...
0
votes
3answers
278 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? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
6
votes
2answers
161 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: ...
0
votes
0answers
74 views

How do I perform the following numerical integration

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
3
votes
1answer
109 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 ; ...
4
votes
1answer
69 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 ...
1
vote
3answers
118 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. ...
4
votes
2answers
264 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
4
votes
3answers
329 views

Find arc length

I am trying to find the arc length for using ...
1
vote
2answers
112 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. ...
4
votes
1answer
95 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 ...
0
votes
0answers
44 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 ...
0
votes
0answers
31 views

NDSolveValue: getting error concerning boundary values

I copied this code from the official website and I get an error when I evaluate it. ...
3
votes
0answers
49 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): ...
0
votes
0answers
48 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
138 views

Is this a bug in NIntegrate?

Is this a bug or I missed something? NIntegrate seems to give a different answer for the same integrand when the option ...
3
votes
1answer
81 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
111 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
66 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
0
votes
1answer
475 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
2
votes
1answer
174 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
votes
2answers
112 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
2
votes
1answer
160 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
votes
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 ...
0
votes
1answer
94 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 = ...
14
votes
1answer
2k views

How to solve a non-linear integral equation?

I have a non-linear integral equation that I'd like to solve with Mathematica: $$ \int_{0}^{1} \mathrm{d}x \frac{B(x) v}{(B(x) + B(v))^2} = 1$$ ...
2
votes
1answer
90 views
1
vote
2answers
632 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. ...
0
votes
0answers
49 views

NDSolve::derarg error: requiring pure function in solving differential equations [on hold]

I'm trying to numerically solve 2 partial differential equations eq1 and eq2 given the boundary conditions in ...
13
votes
5answers
285 views

Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral NIntegrate[Sqrt[r] Abs[Cos[(k + 1/2) Pi r]], {r, 0, 1}] getting as a result 0.413232 for ...
5
votes
2answers
143 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
110 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: ...
4
votes
2answers
379 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
2
votes
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. ...
-3
votes
1answer
287 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 ...
6
votes
3answers
88 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
42 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 ...
3
votes
2answers
105 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...
0
votes
1answer
130 views

Help using NIntegrate

I need some help with NIntegrate. I pasted the code that I wrote below; I know that up to "de" is correct. What I would like to do is NIntegrate de w.r.t phi{0,0.1} and curlE{-10,10}. The final ...
0
votes
0answers
38 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 ...
7
votes
2answers
167 views

Why is mathematica giving wrong and incomparable results for the integral?

1) Integration of Gaussian Distribution with $(x,y,z)$ ranging from $-\infty$ to $\infty$ gives 1 as expected using this command in mathematica. (Total Probability = 1) $\sigma = 200000$ and ...