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3
votes
1answer
85 views

Inverse advection-diffusion problem, solving for a drift coefficient with experimental data?

I am investigating a physical process where I believe the 1-D advection-diffusion equation: \begin{equation} \frac{\partial u}{\partial t} = -\frac{\partial}{\partial x}[\mu(x,t) u(x,t)] + ...
3
votes
0answers
187 views

Numerical integration of acceleration experimental data

I have a vector containing acceleration measurements and the corresponding vector of times in which measurements are taken. To obtain velocity and displacement I used the cumtrapz() function already ...
0
votes
1answer
32 views

Implicitly defined univariate function

So my fellow numerical computational peeps it may be that I am suffering from sleep deprivation but I'm struggling to numerically compute a function $u \rightarrow h(u)$ defined implicitly as follows: ...
6
votes
2answers
104 views

Evaluating 6D Gaussian Integral in Matlab

I have to compute the accuracy of a new Gaussian mixture fitting algorithm. One of the tests include computing the probabilities in certain intervals in a 6D hyperspace. Also, the integral of the ...
1
vote
1answer
28 views

replace non-smooth discrete values with analytical function

I do have a Diffusion coefficient in a convection diffusion PDE which is discontinuous and looks like (concentration on the x-Axis): For numerical reasons i use the integrated form: I calculate ...
0
votes
3answers
160 views

Looking for ways to speed up the numeric evaluation of a symbolic expression in Matlab

{Summary: I have a symbolic expression DCritnF expressed in terms of two variables x1 and x2. I need to find it's numeric value and I used combination of double and subs as given below. ...
5
votes
1answer
90 views

Scheme to alleviate (numerical?) instability in system of coupled nonlinear ODEs

I'm solving a system of nonlinear ODEs that take the form $Q_{nm} \ddot{y}_m + S_{nkl}\dot{y}_k\dot{y}_l +V_n = 0$ where Einstein summation is assumed, $y_i$ are the dependent (complex) variables, ...
1
vote
1answer
87 views

RATTLE numerical integrator example

I want to understand how the RATTLE algorithm works. Can somebody give me an example (in pseudocode or using any programming language like python or matlab) of how would I implement a numerical ...
3
votes
1answer
146 views

C# implementation of the gamma function that produces correct answers at positive integer inputs?

I need a C# implementation of the gamma function that produces correct exact answers at positive integer inputs. I took a look at MathNet.Numerics Meta.Numerics. In both cases, if you calculate ...
9
votes
3answers
810 views

Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
-1
votes
1answer
178 views

Pde problem with robin boundary condition

I have my pde 2D problem with robin condition (form: du/dn +ku=g) to solve with matlab. i have the exact function u and I want to find the function g in robin condition. How can i do it? thanks for ...
5
votes
2answers
94 views

Second derivative of the Associated Legendre functions

I would like to compute, as part of the solution of the Laplace equation using the Fast Multipole Method, the second derivative of the associated legendre functions of the first kind . Specifically, I ...
10
votes
2answers
153 views

Numerical method for equation solving that works on stochastically computed functions

There are many well known numerical methods for solving equations of the type $$ f(x) = 0, \quad x \in \mathbb{R}^n,$$ e.g. bisection method, Newton's method, etc. In my application $f(x)$ is ...
4
votes
0answers
74 views

Why do I get “estimated error” -1.#IND when doing BICGSTAB linear solver using ILUT perconditioner in eigen

I'm using Eigen (a C++ library for numerical linear algebra) to solve a linear equation with the the bi-conjugate gradient BICGSTAB algorithm with Incomplete LU preconditioner. However, the result ...
4
votes
1answer
200 views

Solving Coupled ODE eigenvalue problem

I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem. The system is something like: $ \tag{1} ...
3
votes
1answer
124 views

Closed form for singular values of 2D Laplacian?

Does anyone know where to find an analytic form for the singular values of the finite-difference approximation to the 2D Laplacian, expressed in matrix form for a square grid? This would be for the ...
8
votes
2answers
215 views

Astoundingly large difference when evaulating trigonometric identity with NumPy

According to Wolfram Alpha and the Sage computer algebra system, the following identity holds: $$ \cos\left(\arctan\left(\frac{l_1-l_2}{d}\right)\right) = \frac{1}{\sqrt{1 + \frac{(l_1-l_2)^2}{d^2}}} ...
7
votes
4answers
275 views

Relevance of fixed-point and arbitrary precision computations

I see very few non-floating point computing libraries/packages around. Given the various inaccuracies of floating point representation, the question arises why there aren't at least some fields where ...
5
votes
2answers
146 views

Imposing invertibility on a Matrix

I have a symmetric positive semidefinite covariance matrix $A$, which is approximately computed as the output of a quadratic regression. I then need to invert $A$, but often it is close to singular. ...
8
votes
3answers
260 views

Regression testing of chaotic numerical models

When we have a numerical model that represents a real physical system, and that exhibits chaos (e.g. fluid dynamics models, climate models), how can we know that the model is performing as it should? ...
4
votes
1answer
84 views

Bounded Variation Spaces

Could someone explain me (roughly) the interest of Bounded Variation (BV) Spaces for PDEs ? Is there any numerical application of those space to real problems or is it just a theoretic way to ...
11
votes
1answer
186 views

Catastrophic cancellation in logsum

I'm trying to implement the following function in double-precision floating point with low relative error: $$\mathrm{logsum}(x,y) = \log(\exp(x) + \exp(y))$$ This is used extensively in statistical ...
31
votes
4answers
835 views

Scientific standards for numerical errors

In my field of research the specification of experimental errors is commonly accepted and publications which fail to provide them are highly criticized. At the same time I often find that results of ...