1. ### Mathematica Solving 2-D partial integro-differential equation

While reproducing a research paper, I came across the following equation, ∂f/∂t−(H(f)(∂f/∂x)=0 where [H(f)] is hilbert transform of 'f.' and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is...
2. ### Physics How is it to work in numerical relativity?

the problems/challenges that you have to face daily are mostly related to code issues with the physics itself? Is there room to improve our knowledge of fundamental physics while working on it? Do you enjoy doing it? why? I'm asking this because I'm considering working on numerical relativity...
3. ### A Spline interpolation degree question

Hi, I working on code that does image tracking with missing pixels, but I noticed that higher ordered spline interpolation is unstable. Found through trial and error that the best result is degree 3, picture related. I always thought that spline interpolation does not display behaviours shown...
4. ### I Non-diagonal metric for testing elliptic PDE solver

Hello, I am working with numerical relativity and spectral methods. Recently I finished a general elliptic PDE solver using spectral methods, so now I want to do Physics with it. I am interested in solving the lapse equation, which fits into this category of PDEs  \nabla^2 \alpha = \alpha...
5. ### How can I be sure of my numerical result?

Homework Statement In this problem you will do numerical computer calculations. A skydiver of mass 75.0 kg jumps out of a plane at an altitude of 30.0 km above the surface of the Earth. His parachute fails to open. Assume there is no horizontal motion and the initial velocity is zero. We...
6. ### I Generating polynomials for a multistep method

Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y) Difference Equation Generating polynomials "Coefficients are normalized either by a_k = 1 or sigma(1) = 1
7. ### A Numerical solution to SE - variational method, many electrons

Hi everyone, I am trying to find electron wavefunction of a system I am working in. Numerical method I choose is the Variational method (VM). This method is convenient to find the ground state of the system. More details are available here. Problem I have can be explained on a very simple...
8. ### Numerical methods that need a guess/approximate solutions

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...
9. ### How to compute the surface height based on normal vectors

Suppose I have already found the surface normal vectors to a set of points (x,y), how do I compute the surface height z(x,y)? Basically what I have are the normal vectors at each point (x,y) on a square grid. Then I calculate the vectors u = (x+1,y,z(x+1,y)) - (x,y,z(x,y)) and v =...
10. ### Algorithm for Numerical approximation to add data points

Hi, I am working on TDR (Time Domain Reflectometry). I send a 7GHz bandwidth fast rising edge (14ns) square wave into a coax. I get a return Signal. I have an ADC with 10Msamples/sec. I am using MPLAB IDE for coding the microcontroller. Now I would like to increase the Points on the...