Questions tagged [numerical-integration]

Questions on the use of numerical functions NIntegrate and NDSolve.

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Problem with a DAE and DiscreteVariables (II)

I continue with a DAE problem similar to another one posted here some days ago. @bbgodfrey offered a solution for the DiscreteVariables problem but now I have a ...
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1 vote
2 answers
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Solution on nonlinear pde with intial condtion

It produces an error. please suggest an alternative solution to the above-coupled pde problem. ...
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1 vote
1 answer
84 views

Solving system of equations including numerical integrals over region

I am dealing with the resolution of a concrete beam. Simply put, it is an equilibrium of horizontal forces and moments. Let's first define some parameters : ...
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1 vote
1 answer
46 views

How to solve the error information in numerical integration and solve Sp?

How to solve the error information in numerical integration and solve Sp? The codes are as follows: ...
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2 votes
3 answers
103 views

Infinite Integral involving a Bessel function

I have trouble evaluating the following numerical integral, $$ \int_{0}^{\infty} d k^{(yz)} \, k^{(yz)} J_{0} \left(d^{(yz)} k^{(yz)} \right) \frac{e^{-i d_x \sqrt{k_R^2 + {k^{(yz)}}^{2} }}}{ \sqrt{...
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2 answers
163 views

Why this integral gives zero?

I would like to compute this integral for a =100, ... ,1500 $$ \int_1^\infty \dfrac{\left(x^2-1\right)^{3/2}}{x} \,e^{-ax}\, dx $$ ...
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  • 601
2 votes
1 answer
109 views

Solving this system of differential equation with NDSolve

I'm trying to solve this system of differential equation (the ones in yellow markers are just constants): The initial conditions for this system are n(0) = NN, na(0) = Na, n'(0) = q(0) = 0, q'(0) = ...
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0 answers
37 views

Analytical integral running slow

I am calculating an integral with Mathematica, but it is running super slow! Do you think there is a way to speed up the computation of A3? Maybe I should define my functions in a different way, but I ...
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0 votes
1 answer
67 views

Need help solving iterativelly a set of transcendental equations with NIntegrate

I have two sets of equations: $q = \frac{1}{\sqrt{2 \pi}}\int dz~ e^{-z^2/2}F(q,\phi;z,\beta,\Delta, J) $ $\phi = \frac{1}{\sqrt{2 \pi}}\int dz~ e^{-z^2/2}G(q,\phi;z,\beta, \Delta, J) $ As you may see ...
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3 votes
1 answer
49 views

Why does NDSolve[] want to treat my equations as Delay Differential Equations?

I use NDSolve command (method->equation simplification -> residual) to solve different sets of Ordinary differential equations (ODEs). It had worked alright till I added rather a simple ...
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0 answers
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Numerical integration takes huge time to run

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8 votes
2 answers
218 views

Problem with a DAE and DiscreteVariables

Cross-posted in Wolfram Community. I am solving an DAE problem with NDSolve. It is a physical problem related to friction forces: one mass on the X axis and ...
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4 votes
1 answer
237 views

NIntegrate fails to converge to desired accuracy

I am calculating an integral with Mathematica. This is the code I am using: ...
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1 vote
1 answer
102 views

How to make an integral and reproduce its graph

How by Mathematica we can make the integral, equation (101) in arxiv:1307.5949 $ H_0(t-t_0) = \int^{\frac{a}{a_0}}_1 ~ \frac{da’}{\sqrt{ \frac{\Omega_r}{a’^2} + \frac{\Omega_m}{a’} + \Omega_\Lambda ...
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1 vote
1 answer
116 views

Compute area enclosed in a curve on a surface

Let's consider a 2D smooth surface embedded in 3D shown in the figure below. The corresponding metric tensor in Cartesian coordinates is \begin{equation} h = \biggr(\matrix{1 + \frac{A^2\pi^2}{4} \sin^...
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1 vote
1 answer
60 views

NIntegrate issue without any singularity

I'm evaluating an integral using NIntegrate, I checked the expression and there shouldn't be any singularity at least on paper. The parameter ...
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-1 votes
0 answers
51 views

Integration does not converge in iteration

I have the following code to find a numerical solution for a singular BVPas attached in the picture. I have the following Mathematica code: (This code of this question can be found at Mathematica does ...
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0 votes
1 answer
88 views

PDE with tangential derivative condition along boundary. NDSolve not working

I'm considering the following PDE $$ \begin{align} \left[\cos\theta\frac{\partial}{\partial r}-\frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right]\left[\sin\theta\frac{\partial}{\partial r}+\...
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0 answers
40 views

Cannot fit data due to NIntegrate errors

Here is the data I am trying to fit ...
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0 votes
1 answer
137 views

How to remove error in NIntegrate

I want to solev NIntegrate in two dimension. But when i run the code i got Throw::nocatch: Uncaught Throw[-HolonomicDifferentialRootReduceDumpy[NIntegrateLevinRuleDumpx]+(...
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-4 votes
0 answers
65 views

I want to solve Integrate [duplicate]

I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. ...
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1 vote
1 answer
83 views

Avoid imaginary result FindRoot

I have a code where I'm using FindRoot for the equation toroottp. I plug in some sample values on ...
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1 vote
0 answers
44 views

Looking for an appropriate method of NDSolve for dynamical system

I am dealing with the numerical solutions of a variety of dynamical systems with integrals of motion. As the example, let me consider the Kuramoto model, which equations of motion are ...
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2 votes
1 answer
54 views

Integration over an implicit region

A question asks me to calculate the following integral using NIntegrate: Calculate the double integral ... where D is the area bounded by the four lines ... With ...
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-1 votes
1 answer
81 views

Getting negative value instead of a positive value [closed]

The function is ...
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0 votes
0 answers
60 views

Getting a wrong plot after NIntegration

I am trying to plot this function numerically. R2T = ...
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3 votes
1 answer
117 views

Speeding up Boussinesq equations solving?

I am working on Boussinesq equation. The notebook can run perfectly for only 0.6 steps and then the calculation starts running slowly after 0.7. All boundary conditions seemed fine. I am unsure if I ...
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3 votes
1 answer
83 views

Problem with NIntegrate a solution of NDSolve

I'm having trouble making a function that uses the result of NDSolve: ...
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  • 189
10 votes
3 answers
2k views

Can Mathematica calculate this elliptic, triple integral?

Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b, 0, 1}, {c, 0, Pi}] I'm using basic plan, it gives me the result like that. The ...
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  • 135
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0 answers
76 views

BVP with 2nd order coupled ODEs

I get the following error messages: Infinite expression 1/0. encountered. Indeterminate expression 0.\ ComplexInfinity encountered. Encountered non-numerical value for a derivative at s == 0.1 ...
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2 votes
0 answers
44 views

Why does Mathematica not know some integrals diverge?

I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent. When ...
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2 votes
1 answer
62 views

NDSolve: there are more variables than equations, underdet

I am working on using NDSolve to solve coupled ODE. The following is the coupled equations. It works fine for sever orders. I used table to generate like 962 couple variables and equations, where the ...
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3 votes
1 answer
162 views

Numerical solution of an advance-delay ODE with multiple advances and delays

I am trying to solve a differential equation of the form ...
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0 votes
0 answers
61 views

I am unable to plot 3D graph of integral function

I am not able to solve this integral ...
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1 vote
1 answer
56 views

How to make the NIntegate of two variables as efficient as possible

I asked my question here (Multivariable NIntegrate gives different value if I integrate it separately), I think the best way to get help is by putting the original code here. So, my question is how ...
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0 answers
47 views

NDSolve overdetermined but I can't see how

Edit: partial answer This confuses me but it is due to some behaviour of pattern matching which just seems wrong to me. An example of the behaviour ...
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1 vote
1 answer
98 views

Multivariable NIntegrate gives different value if I integrate it separately

I have a double variable integral, so I can define a function which is the integration of the other variable, and finally, I integrate the other variable. here is the code: ...
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0 votes
0 answers
74 views

Too big error of numerical integrate

I want to do some numerical integrate with Mathematica, but the results are very different from others' result calculated by C code. Here is my code: ...
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3 votes
1 answer
103 views

Inconsistent results between NIntegrate and Integrate

I get these inconsistent results What is going wrong? Fast oscillating terms? Small exponential factors? But then, why the result seems to toggle between values 1 and 2, rather than being a real ...
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  • 347
0 votes
1 answer
49 views

Solution of NDSolve evaluates pointwise, but won't plot (possibly due to issue with FindRoot and replacement rules)

I'm trying to solve a pair of uncoupled differential equations using NDSolve, where the initial conditions are determined by FindRoot. Here's the relevant section of the code, including error message. ...
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1 vote
2 answers
106 views

Integration of accelerometer data to x-y-z position [closed]

Hi I have a list of accelerometer data, in their xyz acceleration values. May I ask how can I integrate these data to get to the position in their xyz angle, assuming the initial velocity is zero and ...
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  • 302
0 votes
1 answer
49 views

NIntegrate can't integrate function but work fine with the expression [closed]

I have a function called psi0 that looks like this: psi0 := E^(-(x - 10)^2/10) and I'm trying to integrate it numerically from 0 to a variable L. However, I keep ...
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0 votes
1 answer
69 views

Problem with NIntegrate and more general problems with NDSolve

I'm new to Mathematica and I'm receiving little help for a (to me) quite difficult problem I'm trying to solve. I want to solve logarithmic Boltzmann equation for abundance of dark matter. I'm having ...
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1 vote
0 answers
58 views

Choosing spatial direction in Method of Lines

Edit:The temporal variable can be set using Method -> {"PDEDiscretization" -> {"MethodOfLines","TemporalVariable" -> t}} ...
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5 votes
1 answer
249 views

Poincare section for a perturbed string

I am trying to find the Poincare section of a perturbed string in a gravitational background with a magnetic field. The plots that I am trying to reproduce are from this paper (page 11). The code that ...
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0 votes
1 answer
63 views

Non Linear System of Diferential Equations with periodic function

I am programming a system of differential equations consisting of 3 cell populations; Normal cells N, Tumor cells T and chemotherapy treatment Q, when a function q is constant. The system is as ...
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0 votes
1 answer
134 views

Numerical integration of highly oscillating function

I want to Numerically integrate the following function ...
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0 votes
0 answers
41 views

How to do double numerical integration one of the variables integrate to another one

Here I have an express with two variables like ...
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2 votes
1 answer
146 views

Simple 3D trapzoidal rule gone wrong

I am trying to implement a 3D trapezoidal rule function, but I get wrong result and I do not understand what's wrong. Here is the code: ...
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4 votes
1 answer
124 views

Nonlinear higher-order equation with fractional derivative in 1d

How can I use Mathematica to solve the following higher order and nonlinear fractional equation? $$\partial_t u(t,x) +\partial_x(u^k(t,x)\partial_x(-\Delta)^su(t,x)) = f(t,x) \quad t >0, \ x \in (\...
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