Questions on the use of numerical functions NIntegrate and NDSolve.

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1answer
58 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
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4answers
88 views
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0answers
45 views

2-Dimensional NFourierTransform

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

Numerical Integration

I have used the following code to evaluate an integral (val) numerically ...
2
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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: ...
7
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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 $h(r)$ ...
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0answers
66 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.) ...
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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 ...
1
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1answer
86 views

NDSolve giving the wrong solution?

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

How do I perform the following numerical integration

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
4
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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 ...
3
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1answer
111 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 ; ...
6
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2answers
162 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
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3answers
329 views

Find arc length

I am trying to find the arc length for using ...
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 ...
1
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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. ...
0
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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
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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
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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): ...
1
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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. ...
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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
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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
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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
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1answer
66 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
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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
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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 = ...
1
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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. ...
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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 ...
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: ...
5
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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: ...
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. ...
6
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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
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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 ...
0
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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 ...
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votes
1answer
289 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 ...
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 ...
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} ...
6
votes
2answers
153 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
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 ...
1
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2answers
80 views

How to integrate a function which is only known at discrete points

I have an integration to do. I want to integrate. $\int_0^\infty sin^2(2\pi t)f(t)dt$ where $f(t)$ takes values from an array in the form $\{t,f(t)\}$ The time steps in the array is 1.1s. Can you ...
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. ...
0
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2answers
128 views

Integral with unreliable result

I want to calculate $\int_R^1 \sqrt{r} |\cos((k+\frac{1}{2})\pi r)|dr $ and I get a result from Mathematica. Then I try to check the result putting the value of $k$ and $R$, (k=1 and R=0.5) in the ...
0
votes
1answer
35 views

Using ImplicitRegion to define an ellipse around Multinormal distribution for integration

I have both a 2D 'MultinormalDistribution', and also a single xy point, and I would like to be able to calculate the probability of this point (given the multinormal distribution) and also plot an ...
1
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2answers
89 views

Evaluation of a large integral

I have a complicated large integral I want to evaluate (does not have a closed form, need an approximation), but Mathematica seems to keep "Running...". Is there any way to make Mathematica use more ...
1
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0answers
46 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
1
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1answer
55 views

Numerically Integrating to find a Maximum using NDSolve

I am trying to numerically find an equilibrium (maximum) of a function using its differential. The following is a simplified version. ...
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 ...