Questions tagged [convergence]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
56 views

Numerical integration of highly oscillating function containing SphericalBesselJ

I am using the following code to integrate my function containing spherical Bessel function. ...
Roy Smith's user avatar
5 votes
3 answers
230 views

Convergence check of a multiple series

I want to check that the following series $$ s_1=\sum_{i,j=1}^{\infty}\frac{ij}{(i+j)^{a/2+1}} $$ diverges for $a\le 6$, where $a$ is a positive integer. I tried with ...
Ruth Murphy's user avatar
1 vote
2 answers
126 views

Integral convergent or divergent?

How can I find out for what values of r (both lower and upper limits), is this integral convergent/divergent? ...
Math_student's user avatar
0 votes
0 answers
139 views

How to solve or test the interval of Uniform Convergence of function series?

How to solve or test the interval of Uniform Convergence of function series? (ref2) e.g. $\sum_{k=1}^{\infty}\left(z^{k-1}-z^k\right)$ The convergence interval of this series can be got by ...
lotus2019's user avatar
  • 2,091
1 vote
0 answers
65 views

Question re recurrence converging limit evaluation

Long time ago I came up with the primitive 2 decimal digits Pi approximation: Pi ~= Sqrt[4 E - 1] see https://oeis.org/A135821 and formula (9) in https://mathworld....
Alex's user avatar
  • 51
0 votes
0 answers
85 views

Error in numerical integration using Wolfram Mathematica

I hope you are doing well. I am having serious problems while calculating a numerical integral in Wolfram Mathematica, as the following error messages appear: 1- "Numerical integration converging ...
Rubens Filho's user avatar
0 votes
0 answers
59 views

How to optimize this multiple sums?

I need to perform this sum $$ \sum_{n_1=1}^{\infty} \sum_{n_2=1}^{\infty} \sum_{n_3=1}^{\infty} \sum_{n_4=1}^{\infty} \frac{K_{1} \left(\frac{a}{x} \sqrt{n_1^2 + 4 y_2^2 x^2 n_2^2 + 4 y_3^2 x^2 n_3^2 +...
Lucas Gondim's user avatar
0 votes
1 answer
88 views

Integral of non-singular cosine apparently doesn't converge

After running the following code I get an error that simple integrals are not converging. I make a false assumption that e>0, and proceed to evaluate the integral over e. Mathematica doesn't ...
Matt Majic's user avatar
4 votes
1 answer
168 views

Why "Repeated convergence test failure" disappears in rare cases while occurring in most runs?

I am trying to solve huge ordinary differential equation of second order using ParametricNDSolve. My code worked fine until I moved to a new model of plasma ...
Igor Kotelnikov's user avatar
4 votes
1 answer
247 views

NIntegrate fails to converge to desired accuracy

I am calculating an integral with Mathematica. This is the code I am using: ...
Riccardo's user avatar
0 votes
1 answer
89 views

Disagreement on Convergence of Integral between Mathematica and WolframAlpha

I am trying to do the integral $ \int_{-\infty}^{\infty} (1+\cos(t))\cosh(t)dt$. Doing this on Mathematica gives me that the integral is equal to 0. However, doing this on WolframAlpha gives me that ...
Zonova's user avatar
  • 341
2 votes
1 answer
197 views

Integrate does not converge while Fourier transform does

Let us say I want Mathematica to compute the integral $$\int dx \, \text{sign} (x) \, \frac{1}{1+x^2} = 0 \, .$$ Indeed ...
MBolin's user avatar
  • 257
1 vote
1 answer
123 views

RSolve unable to solve the equation

I gave the following code as input: RSolve[x[n + 1] == 1/2 x[n] + 2 Log[x[n]], x[n], n] Mathematica gave the same output: ...
coconut2000's user avatar
1 vote
1 answer
109 views

Numerical integration does not converge

...
mathfreak13's user avatar
1 vote
2 answers
274 views

Check the convergence of double sum

I have the following double summations: Sum 1 : $\sum _{p=0}^{k-1} \left(\frac{\sqrt{\frac{(p+1) \Gamma \left(p+\frac{11}{4}\right)}{\Gamma (p+2)}}}{(p+2) \sqrt{\Gamma \left(\frac{11}{4}\right)}}-\sum ...
honeybadger's user avatar
0 votes
1 answer
80 views

Increase convergence near singular point

I have this integrand given by tinteg[z,zm,zh] where I want to integrate it in the range [0,zh]. However, the integrand is ...
mathemania's user avatar
2 votes
0 answers
85 views

NSum complaining of being non-numerical

I am trying to evaluate the sum $\sum_{k,l=1}^{30}\frac{1}{(k^2+l^2+1)^{5/4}}$ so I write NSum[1/(1 + k^2 + l^2)^(5/4), {k, 1, 30}, {l, 1, 30}] but I get a message ...
Chris's user avatar
  • 983
2 votes
1 answer
256 views

NDEigensystem convergence and comparison to DEigensystem

Consider the following eigenvalue differential equation $$ -u_n''(x)+x^2u_n(x)=E_nu_n(x),\qquad x\in(-\infty,\infty). $$ If you know a little bit of physics, you would know that this is the ...
ghost's user avatar
  • 381
0 votes
2 answers
106 views

Calculating the convergence value of summation

Could you please tell me what value the left side of the inequality converges to? (H and P are constant values greater than 2 and n can go to infinity) $$\sum_{n=1}^...
Arash's user avatar
  • 123
0 votes
3 answers
198 views

Convergence and efficiency of 5-dimensional numerical integral using “GlobalAdaptive”

We have a 5-dimensional integral arising as a solution to a physics problem, where two dimensions of the integration space cover the spherical and azimuthal angle, and three dimensions are needed to ...
A. Chitzac's user avatar
5 votes
1 answer
226 views

AceFEM: Divergence in iterative procedure (Newton-Raphson) for fine meshes

I am trying to model a problem of a nearly incompressible $10~\rm{m} \times 2~\rm{m}$ beam with a uniformly distributed end load. The beam has a Young's modulus of $200~\rm{Pa}$ and a Poisson's ratio ...
DvanHuyssteen's user avatar
0 votes
1 answer
153 views

How to do a convergence test on a complex series in Mathematica

I set the following to N=5, and want to do a convergence test on u: ...
Vangsnes's user avatar
  • 571
3 votes
2 answers
111 views

Does this sum converge, and why?

Mathematica says the following sum Sum[(mm Gamma[mm])/ Gamma[-(1/2) + mm] - (mm^(3/2) - (3 Sqrt[mm])/8 - (7 Sqrt[1/mm])/ 128), {mm, 1, \[Infinity]}] ...
esches's user avatar
  • 147
0 votes
1 answer
175 views

Laplace Transform - Differentiation in Time property demonstration

I have a signal x[t_]=t/3 Exp[-3t] UnitStep[t] and the laplace transform as ...
Aditi Sharma's user avatar
0 votes
2 answers
126 views

How to eliminate error: Numerical integration converging too slowly

While doing numerical integration, I am getting a result with the following error messages: ...
Arghya Datta's user avatar
6 votes
2 answers
220 views

Convergence Rate of NDSolve by Increasing the Spatial Grids

I have a very simple PDE equation, with an analytical solution (exact solution). And I want to play with NDSolve and increasing the number of Spatial Grids. Here is the exact solution:(Analytical ...
Nam Nguyen's user avatar
  • 1,751
1 vote
1 answer
241 views

How can I determine the convergence rate of recurrence methods?

I want to solve the equation $x^{3}-x-1=0$ by iterating recurrence equations. I have two different recurrence relations for solving this equation: $x_{k+1}=\sqrt[3]{x_{k}+1} \quad(k=0,1, \cdots)$ $...
A little mouse on the pampas's user avatar
2 votes
2 answers
193 views

How to judge whether the series is absolutely convergent?

I need to judge whether the series $\sum_{n=1}^{\infty}(-1)^{n}\left(1-\cos \frac{\alpha}{n}\right)$ (α>0) is absolutely convergent. ...
A little mouse on the pampas's user avatar
0 votes
1 answer
123 views

Why is the function `SumConvergence` not valid for simple power series

I want to find the convergence interval of function $\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{x^{n}}{n}$. ...
A little mouse on the pampas's user avatar
2 votes
1 answer
2k views

How to get the convergence radius of the result of Series? [duplicate]

The Taylor expansion of function is very useful, but the convergence radius of power series results after Taylor expansion is also important. But the result of ...
A little mouse on the pampas's user avatar
0 votes
1 answer
254 views

How to verify whether the abnormal integral is convergent or divergent?

How to verify the convergence and divergence of the abnormal integrals $\int_{0}^{1} \frac{\sqrt[m]{\ln ^{2}(1-x)}}{\sqrt[n]{x}} d x$: ...
A little mouse on the pampas's user avatar
6 votes
1 answer
373 views

Improving mesh and NDSolve solution convergence

I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
kjcole's user avatar
  • 353
1 vote
1 answer
64 views

Speeding up simultaneous numerical integration where some integrals vanish

I would like to carry out a number of numerical integrals in the form of a table: ...
Chris's user avatar
  • 983
0 votes
0 answers
93 views

Plotting a complex integral function [duplicate]

Can anybody help me to plot the T1 and T2, please? The problem is that the integral part becomes so huge or indeterminate at ...
Ismatov Tolib's user avatar
3 votes
2 answers
301 views

Code that produces plot in V5 doesn't work in later versions

I have problem in plotting Integral function. I can compute/plot the graph of this integration below in Mathematica 5.0, but it is not possible to plot it in higher Mathematica versions. My code is: <...
Ismatov Tolib's user avatar
2 votes
2 answers
405 views

Why doesn't Mathematica provide an answer while Wolfram|Alpha does, concerning a series convergence?

Among other series I've been working on, I was asked to find whether $$\sum_n 1-\cos(\frac{\pi}{n})$$ converged, and Mathematica's output to ...
Albert's user avatar
  • 121
0 votes
0 answers
61 views

Nintegrate providing results much smaller than what is expected

This is the first time I am posting something here. So, apologies if I make any mistake. I am dealing with a numerical integration in Mathematica-11.0 that has a Bessel function in it. In order to ...
user3221839's user avatar
5 votes
2 answers
835 views

Bug in Integrate?

In v. 11.1.0.0 Mathematica for Linux Integrate[Sin[Cosh[t]], {t, 0, Infinity}] returns Integrate::idiv: Integral of Sin[Cosh[t]] does not converge on {0,[...
Mat's user avatar
  • 293
5 votes
1 answer
372 views

Wolfram Language 12 says this absolutely convergent series does not converge. Is there any similar example?

I am reading "Lectures on complex function theory" by Takaaki Nomura. In this book, there is the following example: $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converges absolutely. But ...
tchappy ha's user avatar
6 votes
1 answer
556 views

Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$

In this sum over $k$ Sum[Sin[k (k - 1)]/k, {k, 1, ∞}] the result still containes the summation index $k$. ...
Dr. Wolfgang Hintze's user avatar
2 votes
1 answer
1k views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
dcydhb's user avatar
  • 615