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# Questions tagged [numerics]

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### 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 ...
691 views

### Finite difference discretization on a circle

I am trying to discretize the differential operator $\frac{d^2}{dx^2}$ acting on $S^1 = [0,1]$ using finitely many points around a circle at $0, \frac{1}{N}, \frac{2}{N}, \dots, \frac{N-1}{N}$. Here ...
234 views

### Solving system of differential equations with interconnected boundary conditions

I am trying to solve the following system of differential equations numerically over the domain $x=0$ to $x=D$. The main difficulty is that the boundary conditions are interconnected and depend on the ...
1k views

### Numerical gradient in spherical coordinates

Assume that we have a function $u$ defined in a ball in a discrete way: we know only the values of $u$ in the nodes $(i,j,k)$ of spherical grid, where $i$ is a radius coordinate, $j$ is a coordinate ...
1k views

### “boundary” vs “interface”?

I am working with biofilm and there are many documents talking about boudary conditions while others talks about interface or both of boundary and interface. So, boundary and interface are the same (...
158 views

### Extended finite element method vs $P_k$-bubble element

Can you show me the main differences between 2 methods? I find out 2 reasons but I don't know they are right or not. XFEM is constructed base on enrichment functions whereas P1-bubble is constructed ...
3k 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?
348 views

### Methods for solving BVP for DAE

I look for a numerical method to solve boundary value problems for systems of differential and algebraic equations of the form F(x,y,y') = 0, G(x,y) = 0, y(a) = ya, y(b) = yb, where y = (y1, y2, ... ...
171 views

### For a non-linear PDEs should the source term be discretised at $u_j$ or averaged over $(u_{j+1} + u_{j-1})/2$?

The non-linear Poisson equation in one-dimension, $$0 = \frac{\partial^2u}{\partial x^2} - f(u)$$ can be discretised as to give, $$u_{j-1} -2u_{j} + u_{j+1} = h^2 f(u_j)$$ where $h$ is the ...
96 views

### Implicit Finite difference scheme for a PDE with only one boundary

I am looking at a few reaction-diffusion equations of the form $\frac{dP}{dt} = D\left(\frac{d^2P}{dr^2} + \frac{2}{r}\frac{dP}{dr}\right) - a(P)$ I know the initial conditions and the boundary ...
217 views

### Is there a method to examine numerical diffusion for non-linear PDE?

I have a nasty non-linear partial differential equation. I wonder if there exists a method that would allow me to examine what numerical errors (like numerical diffusion or dispersion) are introduced ...
2k views

### How to plot orbit of binary star and calculate its orbital elements?

I have a set of dates, position angles ($\theta$) and angular separations ($\rho$) for visual binary star. For example: ...
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### Finite element discretization of Reaction-diffusion problem with Dirac source term

I'm writing a code using continuous piecewise linear finite elements on triangular grids to solve the diffusion-reaction problem. the source function f is a Dirac mass at the center. How can i compute ...
239 views

### Can one use incompressible flow approximation for fluid flow in heated pipes?

I was wondering if the use of incompressible flow approximation for fluid flow in heated pipes is reasonable. A previous question (Definition of incompressible flow) seemed to focus on Natural ...
989 views

### Numerical methods for inverting integral transforms?

I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_0\left(xy\right)f(x)\;\mathrm{d}x$$ So for a given $F(y)$ ...
6k views