# Questions tagged [numerics]

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### Is using Monte Carlo method a good approach for solving Boltzmann equation?

I'm trying to solve for electron and hole distribution function using Boltzmann equation with various scattering mechanisms. Since I land up with an integro-differential equation, analytical solution ...
438 views

### ENO-WENO Schemes: Are ENO-WENO schemes non oscillatory for all kinds (linear/non linear) of problems?

Is there an rigorous proof of ENO-WENO schemes being non oscillatory?
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### How should non-constant coefficients be treated with finite-volume first order upwind scheme?

Starting with the advection equation in conservation form. $$u_t = (a(x)u)_x$$ where $a(x)$ is a velocity which depend on space, and $u$ is a concentration of a species which is conserved. ...
1k views

### Optimal ODE method for fixed number of RHS evaluations

In practice, the runtime of numerically solving an IVP $$\dot{x}(t) = f(t, x(t)) \quad \text{ for } t \in [t_0, t_1]$$ $$x(t_0) = x_0$$ is often dominated by the duration of evaluating the right-...
399 views

### Oscillations in singularly perturbed reaction-diffusion problems with finite elements

When FEM-discretizing and solving a reaction-diffusion problem, e.g., $$- \varepsilon \Delta u + u = 1 \text{ on } \Omega\\ u = 0 \text{ on } \partial\Omega$$ with $0 < \varepsilon \ll 1$ (...
1k views

### Integration of an indefinite integral: matlab precision problem

The integral I need to evaluate is: $$\int_x^{\infty} \frac{t^n}{e^{t} -1} dt$$ After some research I found a paper saying, The numerical values of the two integrals [...] are easily calculated ...
212 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 <...
811 views

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### 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 ...
110 views

### How to compute the sum of a power series in a more robust way? [closed]

In order to compute the sum of a power series, we can use for loop, while loop or the analytic formula. I am wondering what is difference between those algorithms and how to improve the robustness of ...
253 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. I'...
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### 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? ...
105 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 ...
163 views

### Computing flux of vector field numerically with regular grids

I would like to compute the flow rate (mL/s) of a pipe flow given the 3D velocity field $\mathbf{v} = (v_x, v_y, v_z)$ over the computational domain (a curved pipe). The field is represented in the ...
430 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 ...
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### 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 ...
I'm working on solving the coupled one-dimensional poroelasticity equations (biot's model), given as: $$-(\lambda+ 2\mu) \frac{\partial^2 u}{\partial x^2} + \frac{\partial p}{\partial x} = 0$$ \...