Questions tagged [mathematica]

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

Filter by
Sorted by
Tagged with
12
votes
1answer
863 views

Replacing Mathematica's QuasiMonteCarlo integration in C++

I have a Mathematica program which performs some integrals in 3 or 4 dimensions using the QuasiMonteCarlo method. The problem is, it takes an annoyingly long time ...
11
votes
1answer
213 views

Numerically Recovering Imaginary Part of Analytic Continuation from Real Part

My situation. I have a function of a complex variable $f(z)$ defined through a complicated integral. What I am interested in is the value of this function on the imaginary axis. I have numerical ...
8
votes
1answer
190 views

What are these oscillations?

I have a function $g(x)$ defined numerically that is sort of in between a Gaussian and a Lorentzian. It decays much slower than a Gaussian, but still faster than a simple inverse power. I need to ...
8
votes
1answer
205 views

Is there a way we can compute my sum involving `subsets` more efficiently?

Suppose we have a countably infinite $A$ and $F_1,F_2,\cdot\cdot\cdot$ are an infinite sequence of finite sets (denoted $\left\{F_n\right\}_{n=1}^{\infty}$) such that $\bigcup\limits_{n=1}^{\infty}F_n=...
7
votes
2answers
547 views

Numerical Green functions for a nonlinear wave equation

I am trying to put down some code to get numerically the solution of the following PDE: $$ \partial^2_t\phi-\partial^2_x\phi+\lambda\phi^3=\delta(x)\delta(t). $$ Of course, there are several ...
5
votes
3answers
10k views

Solving two coupled non-linear second order differential equations numerically

I have encountered the following system of differential equations in lagrangian mechanics. Can you suggest a numerical method, with relevant links and references on how can I solve it, and the ...
5
votes
1answer
3k views

Laplace's equation problem in Polar Coordinates (Edit)

Is there public code in Matlab for solving the Laplace equation in polar coordinates in a circular domain? I tried a lot but my level of Matlab and Mathematica is not good enough, but still not ...
4
votes
2answers
280 views

Writing a programming code directly from the mathematical formula?

For using any programming language, a mathematical formula should be written in the corresponding code. I wonder if there is any service (for any programming language, Matlab, Mathematica, Python, etc)...
4
votes
1answer
3k views

How to compute the Helmholtz decomposition of 2D and 3D vector fields?

I have a sample of 100 particles with their 3D positions and velocities. I want to decompose the velocity vector field to its curl free and divergence free components. Is it a feasible to do so for ...
4
votes
2answers
2k views

Implementing a finite difference method in Mathematica

I am trying to iterate the following equation $$ x_{k}(n+1)=x_k (n)-\epsilon (x_{k+1}(n)-2x_k(n) +x_{k-1}(n))+\sqrt{\epsilon}\; \eta_{k}(n) $$ where $n$ denotes which time step I'm on and $k$ is the ...
4
votes
1answer
76 views

Migdal Recursion and Mathematica

I am studying $SU(2)$ lattice field theory, and I am attempting to use migdal recursion for renormalization. The main equation for Migdal recursion for my case is $$e^{-S_p(U,\lambda a)}=\left[ \...
3
votes
1answer
153 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In addition, I ...
3
votes
1answer
228 views

How does Mathematica compute 'Reduce'?

I submit a Reduce command and get results like this: ...
3
votes
1answer
1k views

Comparing Eigenvectors, Mathematica vs. Matlab

I am trying to create the same outputs in Mathematica and Matlab, however I am running into trouble aligning the eigenvectors with the eigenvalues, I think the Matlab is doing something slightly more ...
3
votes
2answers
339 views

Solving coupled PDEs numerically on a semi-infinite domain with no-flux boundary conditions

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu L_{xx}+...
3
votes
2answers
328 views

Numerical solution of fractional integro-diffrential equ. using collocation method?

problem comes from "Numerical solution of fractional integro-differential , equations by collocation method , E.A. Rawashdeh, Department of Mathematics, Yarmouk University, Irbid 21110, Jordan" $D^...
3
votes
0answers
80 views

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
votes
2answers
44 views

The region of allowed values ​​for solving the equation in Mathematica

In[2]:= Solve[sqrt(2x-9) == sqrt(4x+3), x] Out[2]= {{x -> -6}} But mathematically there is no solution, since sqrt (-21) is not defined. There is a flag that ...
2
votes
1answer
332 views

Mathematica NIntegrate function in C++

I am working on computing a challenging integral. I am working with someone else who wrote some code in Mathematica to compute it. I do not have mathematica so I am trying to do the same thing in C++. ...
2
votes
1answer
346 views

A programming model for Quantum Mechanics angular momenta in Mathematica

I'm writing prototypes for solving the Liouville Equations with Mathematica and C++. Perhaps the question about this may not be suited for this forum in a strict way, but it suits the people here ...
2
votes
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
votes
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
vote
2answers
173 views

How can I learn Scientific Python?

I am an intermediate user of Matlab and Mathematica, but I would really love to start learning Python language for scientific purposes (I am interested in Maths and Physics). Could please someone ...
1
vote
1answer
182 views

Can a second-order ODE be "inconsistent" with its boundary conditions?

I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it $x$. For now, I've managed to approximate away some of the ...
1
vote
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
vote
0answers
98 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
vote
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
vote
0answers
121 views

Nonlinear 2D thermoconductivity equation(numerical solution) [closed]

I have to write a solver for 2D equation: $$\partial_t u = u^2(\partial_x ^2 u + \partial_y ^2 u)$$ I try to use explicit method: $$\partial_t u = \frac{u_{i,j}^{k+1} - u_{i,j}^k}{\tau}$$ and $$\...
1
vote
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
vote
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) <...
1
vote
0answers
182 views

Symplectic Partitioned Runge Kutta method in Mathematica [closed]

I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ \frac{\mathrm{d} Q}{\mathrm{d} t}=\frac{\partial H}{\partial P} \\ \frac{\mathrm{...
1
vote
0answers
76 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
vote
0answers
34 views

How can i get this number set to be recooperated from a product sum? [closed]

W==a(x)=2*(W* x)/41; I'm attempting to make a new type of compression algorithm. A rubber band ball type. I'm trying to make a software that extracts, from that formula, the secret volumes of number ...
1
vote
0answers
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: $$f(t)=\int_{-\infty}^\infty Exp\{it(\omega_H-\omega_l-\omega_k) - \sum _{j\neq(l,k)} S_j [1-e^{-it\omega_j}]\}\, dt$$ ...
1
vote
0answers
55 views

Malliavin Derivative with Mathematica is it possible? [closed]

From mathematica.stackexchange: Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form $$F=F(\...
0
votes
2answers
340 views

Matlab, Mathematica & LAPACK returning 3 different eigenvectors

(I'm not sure which of math.se / stackoverflow / scicomp.se is the right place to ask this question) I have a C++ code which generates a complex matrix and then calculates its eigenvalues and ...
0
votes
1answer
59 views

Problems with the time-dependent Schrödinger equation solutions

I have this Mathematica problem that solves numerically the time-dependent Schrödinger equation in a box: ...
0
votes
1answer
55 views

why on wolframAlpha I cannot find the value of an expression?

I would like to calculate the following two expressions using Wolfram Alpha: $$z = (x (d^2 + d (4 y - 6) - 8 y^2 + 12 y - 3) + 6 (d - 1) (y - 1) y)/(d^2 - 2 d y + 4 y^2 - 6 y + 3)$$ and $$w = -(\...
0
votes
1answer
84 views

ISING2D with Mathematica. Searching a correct way to compute the heat capacity (mean values over several iterations)

I'm trying compute the heat capacity $C_v$ out of my simulation for the 2D-Ising model which is given by $C_v = \frac{\langle E^2 \rangle - \langle E \rangle^2}{T^2N^2}$ ($E$: Energy, $T$: ...
0
votes
1answer
167 views

Numerical solution of nonlinear thermoconductivity equation

I have to find and plot a numerical solution for the following equation (I have to write a solver): $$u_{t} = (u^2 u_x)_x$$ with the following conditions $u(0,t) =0, u(1,t) = \sqrt{\frac{2c-2}{t}}, u(...
0
votes
2answers
448 views

How to interpolate a set of points with a continuous closed B-spline curve?

I have been learining the NURBS theory by the classical textbook "The NURBS Book" this year. In the chapter 9, the author introduced the method of non-rational B-spline curve interpolation ...
0
votes
2answers
3k views

Most efficient library to diagonalize exactly large hermitian or unitary matrices

I am working on a physics problem which requires obtaining the exact eigenvalues and eigenvectors of Hermitian and Unitary matrices numerically. Naturally I would like to ask the experts what are the ...
0
votes
1answer
26 views

Software to find zero divisors of a ring

Are there some programs with packages that help to list all zero-divisors of the ring we desired? especially for the ring of Gaussian integers modulo $n$, $\mathbb{z}_n[i]$. Also want to find which of ...
-1
votes
1answer
62 views

Apply method of manufactured solution into fractional order compartment model

I am trying to solve a fractional-order 2-compartment model using the method of manufactured solution (MMS). I do understand the concept of MMS, but I am not sure how to come with a Mathematica code ...
-2
votes
2answers
129 views

Numerically solving differential equations, the domain is very long, [0, +10^6), so the calculating time is very long

Is there any method to deal with this problem? I am using Mathematica to solve the differential equations, but the calculating time is so long because of the large domain $x\in[0,10^{6})$. In fact I ...