Questions on the use of numerical functions NIntegrate and NDSolve.

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475 views

I ran into an error when I was trying to solve a PDE with a piecewise initial condition by NDSolve

This is a very simple one-dimensional heat-conduct equation, the only special part of it is the piecewise initial condition: ...
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2answers
142 views

Problem with FindMinimum

I am struggling with a problem on fitting a function to my data using FindMinimum. The problem is related to small angle x-ray scattering and my approach is the following: I define the electron ...
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1answer
56 views

Finding the true expectation

I have the density function and I want to determine its expected value ...
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1answer
147 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
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1answer
81 views

Two dimensional high oscillated numerical integral

I have some problem with two dimensional integral. I want to calculate such integral. ...
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2answers
56 views

Incomplete Integration in Area

Area[2 Sqrt[(1 - p^2)^2 - r^2], {p, 0, 1}, {r, 0, 1 - p^2}] is able to perform only the integral over r, leaving the integral ...
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1answer
27 views

NIntegrate is it possible to evaluate the integral using a user-defined grid?

I am using the NIntegrate function and I would like Mathematica to perform the integration in accordance with a grid I define that is sampled uniformly between the boundaries of integration. Let me ...
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1answer
66 views

Strange integration

I tried to evaluate this line Integrate[((-I/2) (E^((-I) x) - E^(I x)) + ((E^((-I) x) + E^(I x)) x)/ 2)/((-1 + E^x) x), {x, 0, Infinity}] Then I get $14$ ...
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1answer
122 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
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3answers
128 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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2answers
96 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 ...
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2answers
98 views

Problem evaluating a complicated integral

Apologies for stating my problem poorly in the first instance, thank you for the help in narrowing down the issue. Problem For those interested, it's for the exact unbiased inverse of the ...
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1answer
276 views

NIntegrate(with singularities) gives different results, which one should I trust?

I am doing an Numerical integral with sigularities. ...
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1answer
150 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 ...
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1answer
219 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 ...
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1answer
153 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 ...
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1answer
197 views

Fast integration of 2D distribution across lines parallel to y-axis

I'm struggling with a small data set and a slow calculation. I have hundreds of small 2D data arrays and need to integrate across several lines parallel to the y-axis. Let me start with the data ...
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1answer
263 views

Which integration strategy to use for this product of polynomials?

What would be the ideal integration strategy for a function like this: $$f(x_1,x_2,\dots,x_N)=\prod_{i=1}^Nx_i^{c_i}\Theta(x_i-p_i)$$ where $x_i,p_i\in \mathbb{R}$, $\Theta$ is the Heaviside function ...
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1answer
86 views

Get unique values for integration limits

For an multidimensional integration I want to build up the integration limits with the following code. (the length of vars is also variable) ...
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1answer
532 views

Problem with NIntegrate in NonlinearModelFit

We are receiving many error messages when using NIntegrate with NonlinearModelFit. Here is a much-simplified version of the code. It arrives at the correct answer after several messages saying that it ...
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1answer
499 views

How to build a grid of integrand points and numerically integrate?

If I have some function I know numerically only, say f(x) and each point $x$ takes significant time to compute so I have them all stored in some file as f(1)=0.232423, f(1.1)=0.3243432,....Then is it ...
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1answer
154 views

How to collect q[t] from the following integration

As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of ...
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1answer
34 views

Problem with NIntegrate over a user-defined region

I define a region as follows: ...
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1answer
72 views

Implicit region misses subset?

Context I am interested in integrating a 2D function over lines defined implicitely Attempt Let me just start by integrating the identify on such sets of lines which a defined using ...
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1answer
100 views

Solving a nasty partial differential equation

I have a differential equation that I would like to solve numerically in the region $z \in [0,L]$ and $t \in [0,t_{max}]$: $$ \partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t), $$ ...
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1answer
98 views

Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
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1answer
141 views

First::normal: Nonatomic expression expected at position 1 in First[0]. >>

I'm trying to do a numerical integration. The integration is within a function. ...
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1answer
64 views

Increase Precision in Numerical Integration

I need to generate a table of Chebyshev expansion coefficients of trigonometric functions (in this case Cos[2 Pi t] to very high accuracy. Code is: ...
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1answer
183 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 ...
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1answer
156 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
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2answers
159 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. ...
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1answer
89 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
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1answer
89 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. ...
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1answer
74 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
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1answer
770 views

Runge-Kutta 2nd Order ODE Solver

Suppose I have a 2nd order ODE of the form y''(t) = 1/y with y(0) = 0 and y'(0) = 10, and ...
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1answer
154 views

Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
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1answer
113 views

Problem with numerical integration

I am not very used to do numerical simulations on Mathematica. I have a problem with numerical integration of this function. Is there any way for this calculation? Input: ...
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1answer
821 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 ...
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1answer
192 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: ...
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1answer
122 views

Numerical integration of Hankel functions

I would like to know how to perform numeric integration for the following type of integrals in Mathematica. For the following integrand, we can not get the symbolic result. ...
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1answer
108 views

PDE plotting assistance needed

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1answer
134 views

Partitioning a numerical integral: need to integrate spectra

I am trying to integrate a spectrum I obtained from a fourier transform infrared spectroscopy experiment, in order to determine the global warming potential of green house gases. In order to do this, ...
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1answer
89 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
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1answer
264 views

Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
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1answer
193 views

Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
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1answer
158 views

Changing ParametricNDSolveValue options for only part of the run

Here is an example of the system that I am running, ...
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1answer
324 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 ...
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1answer
254 views

NIntegrate converging too slowly when increasing size of array

I have a problem with a numerical integration. I have a 4x4x4x4 array that has for each entry an integral and I want to use NIntegrate to evaluate it. It gives me ...
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1answer
267 views

What do these error messages mean when numerically solving differential equations?

I am using Mathematica to numercially solve the following equations: ...