Questions tagged [mathematica]

A powerful mathematical programming software with high level symbolic manipulation capacity.

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Calculate the Bloch wave

The eigenvalue problem $$\frac{d^2u}{dx^2}+2i k\frac{du}{dx}-[k^2-6\sin(x)^2]u(x)=-\mu u(x)$$ gives the first five eigenvalues with $k=0$ or $k=1$ which are $2.06$, $2.26$, $5.16$, $6.81$, and $7....
2
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0answers
47 views

Does the time-dependent 1D advection-diffusion with point sources have an analytical solution?

I am looking for the analytical solution of 1-dimensional advection-diffusion equation with several point sources, Q, along the axial length of a cylinder through which the fluid flow occurs. Neumann ...
2
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0answers
149 views

What could be causing multi-dimensional numerical integration inconsistency?

I'm trying to numerically integrate a multi-dimensional expression. The integrand is complicated; for example this is the integrand for $N=4$: $$\begin{aligned}&x_1^6x_2^5x_3^3x_4^2(x_1-x_1x_2)(...
1
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0answers
81 views

What is the limit involving `Sum`, `Subsets`, and `RankedMax` as `t` approaches infinity?

Motivation Suppose we have a countably infinite $A$ with order and group structures and suppose $F_1,F_2,\cdot\cdot\cdot$ are an infinite sequence of finite sets (denoted $\left\{F_n\right\}_{n=1}^{\...
1
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0answers
99 views

implementation for coppersmith matrix multiplication

Is there any online implementation for the coppersmith matrix multiplication I have searched alot but can not find any? and if there is not any why is that Isn't this algotithm much faster than ...
1
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0answers
113 views

Band structure of nonlinear Schrodinger equation with one dimensional potential

I have a nonlinear Schrodinger equation which reads: $$ \frac{1}{2} \frac{d^2u}{dx^2}+ |u|^2u + V(x)u = -i \frac{du}{dz},$$ where $V(x)=\cos(wx)+ i a \sin(wx)$ and $w$, $a$ are numbers. How to ...
1
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0answers
691 views

Numerical Double integration with endpoint singularity in scipy Python gives incorrect answer

I am trying to integrate the following function in Python, $\int_{0}^{\infty}\int_{0}^{\infty} \dfrac{e^{-x-y}}{B(x,y)}dx dy$, where $B(x,y)$ is the beta function - $B(x,y) = \int_0^{1}a^{x-1}(1-a)^{...
1
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0answers
59 views

CAS Problem with integrals

I got this problem thrown at me, unfortunately I lack context at the moment but I thought Maple or Mathematica would solve it anyways. I have a function $f$ over $x$ and $y$ such as this (Maple) <...
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77 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
1
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161 views

Stationary phase approximation for an integral with infinity saddle points?

I need a hand with the numerical evaluation, in Mathematica, for this integral: $$f(t)=\int_{-\infty}^\infty Exp\{it(\omega_H-\omega_l-\omega_k) - \sum _{j\neq(l,k)} S_j [1-e^{-it\omega_j}]\}\, dt$$ ...