Questions tagged [pde]
Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.
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questions with no upvoted or accepted answers
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Sequential approach to solving coupled PDEs
I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form:
$$
-\nabla\cdot(D_{1}(u_{2},...
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10
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240
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Time advance in Adaptive Mesh Refinement method
I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
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What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
8
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How to construct an effective preconditioner for this particular problem
A quick introduction to my problem
I am currently developing a method for simulation of water waves in three dimensions based on potential flow theory. The computational bottleneck of the method is ...
- 115
6
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FEM : energy minimization VS PDE solving
Engineering FEM
When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as:
Multiply your PDE with a test ...
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Strategy for solving a non-trivial differential equation
I would like to numerically solve an equation of a type as shown below. Does anyone of you have an idea how to approach such a problem? Any links to literature or for further reading would be greatly ...
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Why does the naive barycentric hodgestar fail?
The discrete exterior calculus is defined first using circumcentric dual cells, because the primal and dual edges are orthogonal and thus the dual cells are convex. This leads to a diagonal hodge star ...
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Evolutionary dynamics in vascularised tumors, PDE-ODE coupled system
I have to solve the following PDE-ODE system
$$ \displaystyle{\partial_{t} n = \bigl[a(s) - b(s)(y - h(s))^{2} - d\int_{\mathbb{R}} n \, dy \; + \; \beta \, \partial^2_{yy} n \;}
\\\\
\...
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Numerical methods for the continuity equation with Sobolev vector field
Consider the continuity equation
$$
\partial_t \rho(x,t) + \operatorname{div} (b(x,t) \rho(x,t)) = 0, \qquad t \in [0,T], \quad x \in \mathbb R^N,
$$
with $b \in L^1((0,T), W^{1,p}(\mathbb R^N))$.
...
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Discrete sine and cosine transform for mixed derivatives
Using sine and cosine transforms to solve Poisson's equation with Dirichlet boundary conditions seem quite standard nowadays (see, e.g., here or Table 2 in this paper). In the case of Poisson's ...
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Using entropy functions for increasing numerical stability
Regarding the numerical stabilization of two-dimensional advection equation,
\begin{equation}
\dfrac{\partial f}{\partial t} + \Big(\dfrac{d\varepsilon_1(k)}{dk}\Big)\dfrac{\partial f}{\partial z}
- \...
- 430
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numerical analysis of a partial integro-differential equation
I have to numerically solve a nonlinear partial integro-differential equation. This is my equation,
$$\frac{\partial y(x,t)}{\partial t}=\int_{-1/2}^{1/2} \frac{\pi\cos u}{\sin\pi u-\sin\pi x} \frac{\...
5
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424
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Frozen coefficient method (von Neumann stability analysis)
Earlier it was considered that frozen coefficients method for Neumann stability analysis for finite difference scheme is more heuristic than rigorous. But I have read some information in a book by ...
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Negative viscosity stabilized by fourth order terms
I am trying to solve a "Navier-Stokes"-type problem where the viscosity is negative. Of course this renders the equation unstable and thus I add a fourth order term, so the entire equation becomes:
$$...
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frozen coefficient vs. constant coefficient
This is a follow up to the question about the method of frozen coefficients. I think it deserves to be a separate question. The frozen coefficient problems are obtained by fixing the coefficients of ...
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