Questions tagged [convergence]

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6
votes
2answers
101 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 ...
1
vote
1answer
74 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: $x_{k+1}=\sqrt[3]{x_{k}+1} \quad(k=0,1, \cdots)$ $...
2
votes
2answers
161 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. ...
0
votes
1answer
47 views

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

I want to find the convergence interval of function $\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{x^{n}}{n}$. ...
0
votes
1answer
66 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 ...
0
votes
1answer
66 views

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

How to verify the convergence and divergence of the abnormal integrals $\int_{0}^{1} \frac{\sqrt[m]{\ln ^{2}(1-x)}}{\sqrt[n]{x}} d x$: ...
6
votes
1answer
173 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 ...
1
vote
1answer
55 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: ...
0
votes
0answers
89 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 ...
3
votes
2answers
264 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: <...
1
vote
0answers
48 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 ...
0
votes
0answers
35 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 ...
5
votes
2answers
749 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,[...
5
votes
1answer
154 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 ...
6
votes
1answer
260 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 $k$. ...
1
vote
1answer
194 views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...