Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
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Trouble implementing switching hybrid system with NDSolve
I'm trying to use NDSolve to simulate a hybrid nonlinear system that switches between different linear behaviors based on states and inputs (i.e. switching from one linear behavior to another) which ...
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1
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Plotting an integral with solving for a specific constant [closed]
Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
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Numerical Integration without giving all values
Is there a way to solve expressions numerically, while keeping other variables.
For example, I want to Integrate the expression below for $\theta p,\theta q$ while keeping other things as it is. The ...
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Method to make this complicated integration from interpolating function? [closed]
Hello I want to do this integral
Mu[Psi_, R_] = Integrate[ D[Integrate[Rp f[Psip, Rp]/Sqrt[R^2 - Rp^2], {Rp, 0, R}], R]/ Sqrt[Psi - Psip], {Psip, Psi0, Psi}]
...
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How to solve the following integrodifferential equation by generic approach?
Consider the following equation:
$$
\frac{\partial f}{\partial t} - p H(t)\frac{\partial f}{\partial p} = \mathcal{I}[p,t], \tag 1
$$
Here, f = f[p,t], with p being ...
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2D and 3D versions of GaussianQuadratureWeights?
The package Get["NumericalDifferentialEquationAnalysis`"]; provides a very useful function ...
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1
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1
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Imaginary Result on NDSolve+NIntegrate
I posted the same question in the Physics StackExchange, wondering if it is physics problem. I haven't received any answers, so I am posting in Mathematica StackExchange to see if it is programming ...
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Trouble evaluating the following integral
I am having trouble performing the following integration which comes from a larger function (let me know if I inputted the code wrong from Mathematica so I can fix it!) and even with assumptions, ...
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1
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How to solve this integral equation numerically?
I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of
\begin{...
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1
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Step problem in NDSolve with FixedStep method
We want to solve a set of ODEs with fixed step, whose size is 1/1000, the related codes are given in the following.
The parameters are given by
...
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Plot after applying NIntegrate
I'm trying to integrate and graph $I$ vs $b$ the following integral (eq. 24 in this paper) in wolfram mathematica
$$ I = \int_{2}^{\infty} \frac{g_i^3 \mathcal{K}_t \mathrm{~d} r}{r^2\left|\mathcal{K}...
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NIntegrate Cos[j x], from -pi to pi, with Method->"Trapezoidal" for j = multiples of 16
The function
NIntegrate[Cos[j x], {x, -[Pi], [Pi]}, Method -> "Trapezoidal"] returns zero (as expected) for any value of j except multiples of 16. Any ideia if this is a bug and how to ...
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Millised numbrid siia on peidetud? [closed]
What nubers are here? Mis numbrid on siia peidetud? Peavad olema koordinaadid.
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Change of variable of a numerically solved integral
I have the following function that numerically integrates a function on the interval $\left[ 2, 100 \right]$
...
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Intensity pattern [closed]
I'm trying to get the following intensity pattern from this paper
In the Newtonian case, the equations for the intensity (eq. 9 and 10 in the article), I put them in Mathematica with the change $b^2 =...
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How to chose appropriate finite limits for NIntegrate?
I want to NIntegrate a function using finite limits so it gives a result as close as possible to a result which I would get making the limit ...
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Plot solution of an integral with parameter
In this article, they solve the following integral
$$ \mathcal{I}_{o b s}\left(\nu_0\right)=\int_{\gamma_i} \frac{(A(r))^{3 / 2}}{r^2} \sqrt{\frac{1}{A(r)}+r^2\left(\frac{d \varphi}{d r}\right)^2} d r ...
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Implementation of SINC filter using Integrate results in incorrect output
Bug introduced in 6.0, persisting through 13.3.1.
This is SINC filter, integrate $|H|^2$ from $-\pi/2$ to $\pi/2$.
MMA CODE, Result = 7.27956e-12
...
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Plotting function defined via NIntegrate is too slow
I have the following functions as solutions of a system of differential equations (for calculation, I used ParametricNDSolveValue)
...
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Galactic rotation speed and density research
Rotation speed of Milky Way looks like this until about 25 kpc
I know the following points to describe this curve
...
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How to make NIntegrate with large integration limit?
I try to double integrate this equation with respect to $b$ and $f$
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Numerical Galerkin method with parametrized interpolation function
modified
Here I try to realize a numerical fit (Galerkin method) using parametrized Interpolation function to fit examplary Exp[x] in a given grid. So far I tried
<...
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NDSolve returns stiff problem and forces extrapolation which gives unreasonable result
I am trying to solve a first order ODE using ParametricNDSolve for getting particle trajectory in a flow around an obstacle. I got an error message that "At t == 221.96028149270003`, step size is ...
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How to calculate and plot this integral? [closed]
Any help to integrate this equation:
$$
\begin{eqnarray}
p(k,q)&=&-16 H^2 q^2\int_{q_a}^q \int_{q_a}^q \frac{1}{\sqrt{H^2-k_1{^2}}}\sinh(\sqrt{H^2-k_1{^2}}(q-b))\frac{1}{H b}
\...
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NIntegrate with periodic sharp peaks
I have a function with periodic sharp peak, say (analytic integration is not possible):
Exp[-20 Sin[x]^2 -20 Sin[y]^2]
and I need to perform numerical integral ...
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1
answer
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Different integral values for analytically same integrals
Consider a function $L$ with parameters $h=0.1,\ D=1.5$
$L(m,x):=e^{-\frac{2\ (\frac{x}{h}-m)^{2}}{D}}$.
While the integrals $\int_{-\infty}^{+\infty}L(0,x)dx$ and $\int_{-\infty}^{+\infty}L(40,x)dx$ ...
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How to improve the speed of the calculation of this numerical-integration?
The integrand includes k, Sin[2theta], and T. k is constant, theta is one of the variables (the other variables are x, y and fi), and T is functions of x, y, theta and fi. I found that it needs more ...
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Integration giving unknown messages
I am trying to integrate the following
Integrate[(Log[1 - t] t^(-(1/2) + eps))/(1 + t),{t,0,1}]
To simplify this I am doing a further transformation ...
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Confusing behaviour of EvaluationMonitor in NIntegrate when integrating on a implicit region
I am dealing with some complex integral and I just need an approximate result(have a precision of about 4 digits) for it. Thus I just need to do the integral by sampling at as less points as possible ...
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Unsolved system of Nonlinear equations (bvp)
I am trying to solve the following system of equations:
$\frac{df}{dr }=\frac{a}{r }\sin{f}$
$-\frac{1}{r}\frac{da}{dr}={\cos{f}-A}$
$\frac{1}{r}\frac{d}{dr}(r\frac{dA}{dr})-\frac{1}{r}\frac{da}{dr }=...
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How to solve "no more memory available" for this code?
In the codes, G is a integration depending on x and y, and tmr is defined as tmr:={x,y,G}. When I export [Table[tmr, {x, -1 * 10^(-8), 1 * 10^(-8), 1.0 * 10^(-9)}, {y, -1 * 10^(-8), 1 * 10^(-8), 1.0 * ...
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How to incorporate boundary conditions?
I have this linearized PDE problem:
$$\lambda a^\ast+\bar{a}v^\ast_z+\bar{a}_zv^\ast+\bar{v}a^\ast_z+\bar{v}_za^\ast=0$$
$$\lambda \bar a h^\ast -\bar a \bar h v^\ast_z-\bar a \bar v_z h^\ast - \bar h ...
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Numerically testing integrals which evaluate to Dirac delta distributions
For non-distributional integrals, it is very useful that one can test integral equations numerically, e.g. if I have some argument to believe that
$$\int_0^{\infty}dx e^{-a x}=\frac{1}{a},\qquad \text{...
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Large step size for ExplicitEuler in NDSolve
I am an educator trying to teach Euler's method to numerically approximate ODEs. I want to use Mathematica to generate somewhat small examples, i.e. a large step size. When I run
...
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Why the NIntegrate can not be worked out?
The integrand includes k, Sin[2theta], and T. k is constant, theta is one of the variables (the other variables are x, y and fi), and T is functions of x, y, theta and fi. I found that it needs more ...
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Event control in delay differential equations
A delay-differential system for variables {y[t],z[t]} is defined by time-lag w
{y'[t] == (r (1 - y[t] - z[t]) - 1) y[t],
z'[t] == (y[t] - y[t - w])};
The ...
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Exponential and logarithmic functions slow the higher iterations in Mathematica
I want to solve bvp given in the (39)-(40) by the method given below these equations. I have written this method in Mathematica as follows. However, for n=1 it print the solution quickly but for ...
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Accuracy of numerical solutions provided by pdetoode
I am interested in solving the following differential equation using pdetoode
(you can find pdetoode here).
...
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Solve Differential Equation Numerically
I investigated my system and encountered differential equation such as
$y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$,
where $d$ is a constant. The boundary condition is
$y'(0) = 30$
$y'(\infty)=0$.
I ...
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Table of integrals involving modified Bessel function of the second kind
I need to compute integrals of the following form as accurately as possible (possibly with extended precision):
$$
I_{nl}(\omega)=\int_0^{1/2}\left(1-x^2\right)^{1/4} \sin (2 \pi l x)\; \sin (2 \pi ...
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Set of differential equations with trigonometric functions and a derivative squared
I've been trying to solve a set of differential equations that involve the square of a derivative, similar to another post I made here, and trigonometric functions, as seen here
\begin{equation} \frac{...
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Evaluation and plot the result of NIntegrate obtained from NDSolve
First I solved coupled ODE using NDSolve. Now I want to integrate the expression (p'''[0] - ((1.0/k)*p''[0]) + (beta*m*m*s[0]) with respect to the parameter ...
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2
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Solving coupled differential equations involving the square of the derivative
I want to solve the following system of coupled differential equations in order to obtain particle trajectories:
\begin{equation} \frac{dt}{ds} = (E-y\, p_t)y \end{equation}
\begin{equation} \...
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Volume of Region Contained by 3D Data Points
I have a dataset consisting of (x,y,z) data that describe a surface, and I need to find the volume of the region bounded by that surface. The data do not follow any mathematical equation, but the ...
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Plot the Integration of an expression that uses the results of NDSolve
I want to plot the Integration of an expression that uses the results of NDSolve. But I am getting a blank window from the following code.
...
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What are some ways to speed up calculations
Below is the code for calculating the eigenfunctions and eigenvalues of the following system:
$HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
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