# 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.

630 questions
123 views

### citations for numerical lookup table interpolation of P/ODE(s) RHS

I'm not sure that this *overflow is right place to ask.... Sorry if it is off topic. Does anyone know a citation (scientific article or book) for a numerical trick (method), when we tabulate a right-...
207 views

### How can I numericaly solve a convection-diffusion equation with a large diffusion term?

I want to numerically solve the advection-diffusion equation: $$u_t(x,t) + cu_x(x,t) = v u_{xx}(x,t)$$ for $x \in [0,1]$ and $t \geq 0$ subject to the boundary conditions ...
117 views

### Stable method for solving a HJB equation

I am considering finite difference methods and their error analysis for solving HJB equation of the following form: $$v_t=|\sigma(x)v_x|,\quad x\in \mathbb{R},$$ where $\sigma$ is a given function ...
113 views

### How one could choose the value of viscous coefficient for obtaining stable solution of Burgers' equation?

Burgers' equation is a fundamental PDE used in various fields such as number theory, gas dynamics, heat conduction, elasticity, etc. It is crucial especially for developing numerical models for ...
44 views

### Degree of freedom for elastic wave propagation problem

I am solving a elastodynamics (vector valued elastic wave) equation. I create the 2D mesh in Gmsh discretised into triangular elements of second order. Therefore, it is my understanding that the ...
87 views

### Which numerical scheme should be used?

Trying to find a way to solve exponentially nonlinear elliptic equation with complex source term i manage to know about such schemes like Godunov, Lax-Friedrich, MUSCL. I still seraching for ...
292 views

### On the Rellich-Kondrachov embedding theorem

Let $\Omega$ be a bounded open set in $\mathbb{R}^d$ where $d \geq 1$ is a positive integer, with Lipschitz boundary. Let $k,l$ be non-negative integers and $1 \leq p < \infty$ then if $k > l$ ...
262 views

### implementation of method of line and Runge-Kutta to the given equation

$$\frac{d^2 u}{dx^2} +A \frac{d^2}{dx^2}\left(\frac{du}{dt}\right)=B$$ I want to solve the equation given above. I need to first discretize it by the Method of Lines and then evolve the resulting ...
135 views

274 views

### Implementing odespy for system of PDEs

After trying to use RK4 to solve the below system of equations, it appears the output had large and fast oscillations even with an adaptive time step I incorporated using the Cash-Karp method. I am ...
76 views

### What is a good algorithm to solve a discrete continuity equation in Cylindrical coordinates?

The equation is: $\partial f/\partial t + \nabla \cdot (v f) = 0$ $, \;\; f \in [0,1]$ and $v$ is a velocity known at every grid cell. A more precise constraint is that $f$ is either 0 or 1 but ...
199 views

### Applying Runge-Kutta to nonlinear system of PDEs

I am applying a 4th order Runge-Kutta code, using the method of lines, to solve the following: $$\frac {\partial y_1}{\partial t} = y_2 y_3 - C_1 y_1$$ \...
272 views

### Stable implicit method to solve convection-heat diffusion in 3D

The last couple of hours I have been looking for an unconditionally stable method to solve the convection-diffusion equation within a 3D inhomogeneous material. Here's the well known diffusion-...