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0
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1answer
56 views

Computing expectations

I want to compute the following conditional expectation $E_{t}[\phi(A_{t+1}, \eta_{t+1})| A_t]$ where $\log A_{t}=\rho \log A_{t-1} + e_{t}$ and $e_{t}$ is IID $N~(0,\sigma_e)$ and $\eta_{t}$ is ...
2
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2answers
82 views

Can the conservative form of the advection equation be re-written by replacing the velocity term with an integral over all other points in space?

Suppose I have a 1D advection equation in conservation (divergence) form $\partial_t u(x,t) = -\partial_x [v(x)u(x,t)],$ where $u$ is a conserved quantity in space, and $v$ gives the velocity of the ...
1
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0answers
30 views

Package for integration over non-rectangular region

I want to compute the expected value of a multivariate function f(x) wrt to dirichlet distribution. My problem is "penta-nomial" (i.e 5 variables) so calculating ...
0
votes
1answer
127 views

Solve a fourth order differential equation

I want to solve $$ \frac{\partial^2}{\partial t^2}u(z,t) + a\frac{\partial^2}{\partial z^2}u(z,t) + k\frac{\partial^4}{\partial z^4}u(z,t) = 0 $$ with $u(z,0) = 1+0.1e^{-\frac{z^2}{2}}$. I'd like to ...
2
votes
1answer
160 views

Solve a differential equation with finite difference method

I want to solve this equation $$ -\frac{1}{2}f''(x)+2a\ f(x)^3 = f(x)\mu $$ One exact solution (there are a lot of different kinds) of this equation is $f(x) = f_\infty \tanh(\sqrt{2a}f_\infty x) $ ...
4
votes
2answers
144 views

Line Integral Convolution (LIC) Requirements

I'm trying to plot some vector fields using LIC technique. More specifically, I'm using the Python solution for this kind of plot. Before applying that approach, I was plotting my vectors as quiver. ...
2
votes
0answers
110 views

Integration of nonlinear PIDE via spectral methods

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
5
votes
2answers
130 views

Periodic Green's functions in integral equation methods in different frequency regimes

I'm asking about the solution of the Helmholtz equation on a periodic domain with piecewise constant wavespeed in different frequency regimes. One possible approach is to solving this problem is to ...
0
votes
1answer
209 views

Matlab: Error in integral function

I want to compute an integral with the following code written in Matlab. ...
5
votes
2answers
129 views

Convergence issues for a non-linear system

I have a nasty system of coupled integral equations, which I managed to discretize and recast a non-linear system, i.e. something like: $$ \vec{w} = F \left( \vec{w} \right) \hspace{32pt} w \in ...
3
votes
1answer
206 views

Finite difference equations versus boundary integral equations for elliptic pdes

In certain cases, boundary integral methods are preferred for elliptic partial differential equations as opposed to finite difference methods. For instance, for solving the Poisson equation in a ...
3
votes
0answers
62 views

analytic or numeric integral of diverging function

I'm trying to carry out the following integral numerically $$\int_{r_\mathrm{in}}^{r_\mathrm{out}} \Sigma\left(r'\right) \frac{r'}{r} \left( \frac{1}{r-r'}\, E(L) + \frac{1}{r+r'}\, K(L) \right) ...
8
votes
2answers
422 views

An Octree Code in Fortran

I am new to scientific computing. I am looking for a Fortran ( preferably f90) implementation of an Octree. My problem requires an Octree which divides my domain until there aren't more than some N ...
2
votes
1answer
114 views

Flux calculation - discretization of solid angle

I am currently tasked with calculating the total flux of photons or irradiance from a flat emitter ('pixel'). Previously we measured the Luminance head-on (90 degree from the emitting surface) and ...
9
votes
1answer
587 views

Numerical integration for modelling curve for superconductors (Python)

I am a physicist who is trying to model the current-voltage characteristics of a superconductor-superconductor junction. The equation for this model is: \begin{align} I(V) = ...
2
votes
0answers
30 views

Lax equivalence theorem for integro-differential equation

Can the Lax equivalence theorem (http://en.wikipedia.org/wiki/Lax_equivalence_theorem) be applied to the discretization of integro-differential equations, or does a similar theorem exist for them?
3
votes
2answers
93 views

Representing an integral as a special function

In my research I have come across the following integral \begin{equation} f = \int_0^{2\pi} \text{d}\theta \exp\left\{\frac{3}{2}(h_1 \cos^2\theta + h_2 \sin^2\theta + 2 h_{12} \sin\theta ...
3
votes
2answers
158 views

What does fundamental solutions stand for in boundary element method?

I gain some introductory knowledge from the materials I read. I feel Ok with the numerical implementation part of boundary element method when the integral equation has been formulated. But the ...
2
votes
2answers
244 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" ...
2
votes
1answer
149 views

Different kinds of Integral Equation Methods

I am relatively new to integral equations for solving time-harmonic EM scattering problems. I have read a decent number of papers on the subject, and it seems that for formulations that can support 3D ...
4
votes
1answer
205 views

Defining electric current source excitations for surface integral equation formulations

In a finite difference (FD) based electromagnetic formulation based on a Yee cell grid, one can define electric current source excitations ($J$) on the $E$ field grid points. At a distance, the fields ...