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96 views

Can I numerically solve these equation in Mathematica?

I have this couple of equations : $ \partial_\mu \partial^\mu z^i + G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) \partial_\mu z^j \partial^\mu z^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{l}} ) \...
0
votes
0answers
24 views

Integrating System of ODE's

I'm trying to integrate the system $$\frac{d}{d z} \left[ \begin{array}{l}{\hat{a}} \\ {\hat{b}}\end{array}\right]=\frac{i \omega}{\overline{c}} \left[ \begin{array}{cc}{\left(\Delta_{l}^{(+)}-1\...
0
votes
1answer
89 views

Complex number as the result of an integral [closed]

My question has been asked before by other members, however, I didn't find the answer to their question helpful in my case. I'm doing a simple numerical integral with real numbers in mathematica, but ...
0
votes
2answers
121 views

Numerically integrate complex valued function of a real variable and a complex variable

I need to numerically integrate a complex valued function of a real variable and a complex variable by the real variable. My integral: $$ \int^1_{-1}\frac{e^{ix}}{x-z}dx ~~~\text{where} ~~x \in \...
6
votes
2answers
192 views

Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
3
votes
1answer
120 views

Complex first-order differential equation

I have a differential equation $\frac{dx}{dt} = \sqrt{1+x^4}$ $x$ is a complex variable. I want to solve it for some given initial condition, and plot the solution (real part vs. imaginary part). ...
10
votes
1answer
229 views

FiniteElement v.s. TensorProductGrid: which is reliable for Schrödinger equation with periodic b.c.?

This is a problem comes up in the discussion under this post and I think it's worth starting a new question for it. I suspect the underlying issue is the same as in this post, but not sure. Consider ...
1
vote
1answer
248 views

Contour integration with Mathematica

I seem to have difficulty getting Mathematica to evaluate contour integrals correctly. I am just parametrising them and inputting them in as usual but I am having problems. For example, consider $I=\...
1
vote
2answers
257 views

Having problems integrating a function of a complex variable [closed]

I've tried to calculate the integral And I got the result $16i \pi ^3$. I wanted to check my calculation, so I ran this code in Mathematica: ...
6
votes
2answers
345 views

How to solve this trigonometric complex ODE system?

The system of nonlinear ODE is $$ \mathrm{i}\,s(\ddot p-\frac{1}{2}\sin{2p}\;\dot q^2)=\mathrm{i}\,c\sin p\;\dot q-a\sin p+b\cos p\cos q\,,\\ \mathrm{i}\,s(\sin^2p\;\ddot q+\sin{2p}\;\dot p\dot q)=-\...
3
votes
1answer
182 views

Real Integrand, Complex Integral result?

I have a function that is real when u is real and positive. And L[u,s,t] is an even function in s and t, and it is non-negative with above conditions. ...
0
votes
1answer
247 views

NDSolve error (not a real number when the arguments are?)

For the NDSolve, I have problem. It seems to be non-zero imaginary part of the number. How can I get over this issue? The following is the script. ...
4
votes
1answer
415 views

Orbit followed by a particle around Schwarzschild Black Hole

The following is a equation which describes various possible orbits of a particle around the Schwarzschild black hole spacetime in general relativity. I want to solve it from ...
0
votes
2answers
169 views

Complex Number Presentation and an issue with FindRoot [duplicate]

First of all, I am not entirely sure what the problem is. The code I am presenting worked in a previous version of Mathematica but not now in Version 11.0.1. Essentially, I am calculating Point Spread ...
1
vote
1answer
280 views

NonlinearModelFit::fmgz: Encountered a gradient that is effectively zero

I am trying to solve a nonlinear parameter fitting problem as described by Mathematica code below: ...
9
votes
1answer
321 views

NDSolve for complex BVPs and FindRoot

NDSolve works for complex valued ODE initial value problems (IVP). However, for a simple boundary value problem (BVP) with complex coefficients it fails: ...
1
vote
1answer
330 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
9
votes
2answers
327 views

Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after 8.0.4 and before 9.0.1, and fixed in 11.1.0. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but Integrate and ...
1
vote
0answers
247 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
21
votes
1answer
996 views

Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
5
votes
1answer
1k views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
6
votes
2answers
556 views

NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$ I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
2
votes
1answer
233 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
2
votes
1answer
304 views

Complex Integration

There are some sequential functions: ...
7
votes
3answers
321 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the following integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, ∞}, Assumptions -> z ∈ Reals] >> -3.36354 - 3.85013 I The output is ...
1
vote
0answers
302 views

A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
4
votes
1answer
584 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be <...
2
votes
2answers
469 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
2
votes
0answers
151 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
5
votes
2answers
2k views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
4
votes
1answer
798 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've spent the last week searching for a way to numerically calculate the pole contributions to this multi-dimensional complex contour integral while avoiding the singularity at z=0: $$ \oint_{C_1(0)}\...
9
votes
2answers
1k views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m \...
9
votes
1answer
3k views

Is it possible to set a variable as a positive one in the whole notebook?

I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end). For example I do ...