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 ...
Cameron Alred's user avatar
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1 answer
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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?
Med Ch's user avatar
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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 ...
Lelouch's user avatar
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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}] ...
Rémy Galli's user avatar
1 vote
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153 views
+500

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 ...
John Taylor's user avatar
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2D and 3D versions of GaussianQuadratureWeights?

The package Get["NumericalDifferentialEquationAnalysis`"]; provides a very useful function ...
Ulrich Neumann's user avatar
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1 answer
98 views

Integration by Numerical Methods

I have a big expression, ...
Lelouch's user avatar
1 vote
1 answer
73 views

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 ...
Saesun Kim's user avatar
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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, ...
MathZilla's user avatar
  • 113
2 votes
1 answer
141 views

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{...
dcmpsr's user avatar
  • 53
2 votes
1 answer
80 views

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 ...
so_sure's user avatar
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1 answer
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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}...
Soliton-104's user avatar
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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 ...
Írio Menezes's user avatar
-4 votes
1 answer
81 views

Millised numbrid siia on peidetud? [closed]

What nubers are here? Mis numbrid on siia peidetud? Peavad olema koordinaadid.
Tiit Künnapuu's user avatar
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1 answer
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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 $\left[ 2, 100 \right]$ ...
Soliton-104's user avatar
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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 =...
Soliton-104's user avatar
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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 ...
Patrycja's user avatar
1 vote
1 answer
257 views

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 ...
Soliton-104's user avatar
4 votes
1 answer
182 views

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 ...
Ring's user avatar
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97 views

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) ...
derdin1's user avatar
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-1 votes
1 answer
135 views

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 ...
Rémy Galli's user avatar
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0 answers
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How to make NIntegrate with large integration limit?

I try to double integrate this equation with respect to $b$ and $f$ ...
Dr. phy's user avatar
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142 views

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 <...
Ulrich Neumann's user avatar
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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 ...
PKD's user avatar
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1 vote
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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} \...
Dr. phy's user avatar
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84 views

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 ...
Frank Wang's user avatar
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1 answer
50 views

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 $\int_{-\infty}^{+\infty}L(40,x)dx$ ...
chintan's user avatar
2 votes
2 answers
102 views

NDSolve of a non-linear ODE

I am trying to solve the following non-linear ODE numerically: ...
Zazu's user avatar
  • 23
1 vote
2 answers
130 views

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 ...
user59546's user avatar
1 vote
3 answers
206 views

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 ...
BabaYaga's user avatar
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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 ...
zhang yixin's user avatar
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1 answer
129 views

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 }=...
Andrey's user avatar
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1 vote
0 answers
54 views

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 * ...
user59546's user avatar
0 votes
1 answer
85 views

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 ...
Fun123's user avatar
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0 votes
1 answer
62 views

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{...
Luke's user avatar
  • 185
3 votes
1 answer
79 views

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 ...
trevork's user avatar
  • 43
1 vote
1 answer
104 views

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 ...
user59546's user avatar
2 votes
1 answer
52 views

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 ...
DavidG's user avatar
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0 votes
1 answer
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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 ...
Junaid Ahmad's user avatar
3 votes
1 answer
151 views

Accuracy of numerical solutions provided by pdetoode

I am interested in solving the following differential equation using pdetoode (you can find pdetoode here). ...
umby's user avatar
  • 585
3 votes
1 answer
130 views

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 ...
이영규's user avatar
0 votes
0 answers
119 views

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 ...
user12588's user avatar
  • 585
1 vote
1 answer
60 views

Slow convergence of 6 dimensional integral in a spherical region

...
user1477339's user avatar
1 vote
1 answer
55 views

Graph lines do not show dashes [closed]

I have the following code of an iteration: ...
Junaid Ahmad's user avatar
0 votes
2 answers
83 views

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{...
MarcelRomp's user avatar
0 votes
1 answer
98 views

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 ...
Dr. B. Mallick's user avatar
4 votes
2 answers
444 views

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} \...
MarcelRomp's user avatar
3 votes
4 answers
305 views

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 ...
John's user avatar
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0 answers
79 views

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. ...
Dr. B. Mallick's user avatar
1 vote
1 answer
77 views

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(\...
Mam Mam's user avatar
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