All Questions
Tagged with computational-physicsdifferential-equations
64 questions
2votes
1answer
82views
Help with approaching a hyperbolic PDE (QED)
This is my first question here, so I'd like to apologize in advance if there's too little, or too much information and for my general lack of "etiquette". I am in need of help with choosing ...
- 21
1vote
1answer
107views
Demonstrate hysteresis of Duffing equation in numerical solution
Objective I would like to model the following Duffing equation using Runge-Kutta 4 algorithm : $$ \ddot{x} + 2\mu\dot{x} + \gamma\dot{x}^3 + \omega_0^2x + \alpha x^3 = k\cos{\omega t} $$ I am using an ...
- 41
-2votes
1answer
72views
Problem solving geodesic equations numerically [closed]
I been having trouble solving the geodesic equations. The end goal is to plot them on a surface. I firstly calculated the Christoffel symbols and then inserted the differential equation in an ODE ...
1vote
2answers
98views
Numerical solution of differential equations, e.g. the three-body problem
What forms of differential equations have numerical solutions with errors that go to zero with sufficient computational power? For example, suppose I want to solve a differential equation $E$ for a ...
- 135
1vote
2answers
89views
Static solution to an implicitly dynamic problem - heat equation
Heat equation This is the heat equation: $ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} $ ...
- 123
0votes
1answer
127views
Solving divergence and curl equations numerically
I've recently come to learn about Jefimenko's general solution for Maxwell's equations as well as the FDTD method in electromagnetic optics, and that has got me thinking whether I myself can solve ...
- 2,164
0votes
1answer
95views
Method of characteristics with coupled ODEs
I am having trouble following the derivation in this paper https://arxiv.org/abs/1810.07775 using the method of characteristics. By using the method of characteristics, they derive the following ODEs ...
- 71
0votes
0answers
66views
How to properly discretize and solve the Liouville equation?
Consider some dynamical system $\dot{\textbf{X}}(\textbf{x},t)=F(\textbf{X})$ where $\textbf{X}$ is discretized along a 1-dimensional spatial coordinate $\textbf{x}=(x_1,\dots,x_N)^T$. Let $\rho(\...
- 101
2votes
2answers
208views
Book on numerical solution of PDEs
I would like to learn how to solve partial differential equations (first and second order, e.g. Poisson, etc...) numerically with finite differences. Which book can be recommended if one want it to ...
0votes
0answers
209views
Physical intuition for the Poisson Equation with Neumann boundary conditions
I am looking at a tutorial using Fenics for solving PDEs using finite element methods. One example that they use is the Poisson equation with Neumann boundary conditions. The equation itself is: $$ - \...
- 181
1vote
0answers
213views
How does convex splitting method work?
I'm an undergraduate physics student and I'm simulating some partial differential equations using finite element method. For non-linear equations I found a method called linear convex splitting ...
- 11
0votes
1answer
635views
Stability of Euler-Cromer method
Euler method doesn't perform well in the context of oscillatory problems like the harmonic oscillator; the amplitude of the oscillation gets bigger with time, which clearly contradicts theory as no ...
1vote
0answers
69views
Numerical integration of wave equation near black hole in Eddington-Finkelstein coordinates
I am studying the spherically symmetric wave equation on the Schwarzschild background in Eddington-Finkelstein coordinates $(v,r)$. I want to numerically integrate the $v$-time-evolution of such a ...
- 813
1vote
1answer
252views
How do you solve any partial differential equation using equivalent circuits? How is this possible?
Here's the quote from this wiki: In 1945 Kron suggested an approach to Schrödinger's equation with networks. The same year he used equivalent circuits to solve differential equations. So I've been ...
- 111
2votes
1answer
250views
How many equations of motion? The higher order derivatives are highly correlated
Note: the bounty text above states "second order linear differential equations". It is an empirical observation that this is the case for the particular system I'm studying, please read &...
- 111
