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# Questions tagged [numerics]

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### Why would someone use empirical sum instead of numerical integration methods?

In the context of a scientific computing application, using data coming from (powerful) embedded systems, acquiring raw data (but from calibrated acquisition electronics), I have been asked to ...
1k views

### Applying Neumann boundaries to Crank-Nicolson solution in python

Consider the heat equation $$u_t = \kappa u_{xx}$$ with boundary conditions of $$u(x,0)=0\\ u(0,t)=100\\ u(l,t)=0$$ Numerical analysis by pyton can be done with ...
111 views

### Calculation of the EFIE integral

I need help computing the following integral: $$\int_{}\frac{(1+jk|\vec{r}-\vec{r}^\prime|)e^{-jk|\vec{r}-\vec{r}^\prime|}}{|\vec{r}-\vec{r}^\prime|}d\vec{r}^\prime$$ in this integral $\vec{r}$ ...
175 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 <...
173 views

### Numerical Lax-Wendroff scheme order of convergence on Burgers equation

I was suggested to move that question here. The question to be as follows. Statement of the problem Is it possible to achieve the second order of convergence (OOC) of Lax-Wendroff (LxW) scheme ...
887 views

### How do you debug numerical code, what could be source of this oscillatory error?

Quiet a lot of insight can be gained form experience, I was just wondering if anybody has seen something similar to this before. The plot shows the initial condition (green) for the advection-...
50 views

### Problems with deriving an equation for a finite-difference scheme given in the journal paper

I'm reading this paper and trying to follow everything that the author has done. A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem But there ...
109 views

### Meaning of a symbol in a research paper

The 2014 paper "Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights" by I. Bogaert (https://doi.org/10.1137/140954969) contains the following expression in Appendix A: What is ...
476 views

### Finite difference method basic implementation on Octave

Trying to study the error of FDM for a second order derivative versus step size I calculated the coefficients and validated them, but the output has errors for small step sizes. The function in ...
125 views

### Implementation details for high order IMEX methods by Kennedy and Carpenter

This question is a continuation of Fourth order IMEX Runge-Kutta method, concerning the implementation. Is seems to me that the first implicit stage value involves a direct evaluation, rather than ...
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