intro 2 fdm & examples
theory
08-apr-2020Persamaan diferensial parsial10-apr-2020Persamaan diferensial parsial dengan spreadsheet
examples
08-aug-2019Diffusion Simulation with JS: Writing Your Own ABM Code27-jun-2020Molecular Dynamics (MD) Method and Agent-Based Model (AMB) in Simulation of Stem Cell Deposition on the Surface with Nanopattern: Simulator Design25-sep-2019Compaction of two-dimensional system of composite spherical particles under influence of self-gravitation: Between lock-and-key model and tetris-structure21-aug-2019Head-on collision of two spherical grains with 2-d internal structure09-aug-2019Simulation of Blood Cell Separation System Based on Inertia and Elasticity using Molecular Dynamics Method (a simulation design)10-jul-2019Molecular Dynamics Simulation of Floating Spheres Forming Two-Dimensional Hexagonal Close Packed Structure29-jun-2019Granular buoyant force in a two-dimensional intruder-particles bed system31-oct-2018Simulation of snake-like swimming system using granular model
bvp with matrix
- Qingkai Kong, Timmy Siaw, Alexandre Bayen, “Finite Difference Method” in Python Programming And Numerical Methods: A Guide For Engineers And Scientists, Academic Press, 1st edition, Nov 2020, url https://pythonnumericalmethods.berkeley.edu/notebooks/chapter23.03-Finite-Difference-Method.html [20231101]
- Equations $$\tag{1} \frac{dy}{dx} = \frac{y_{i+1} - y_{i-1}}{2h} $$ $$\tag{2} \frac{d^2y}{dx^2} = \frac{y_{i+1} -2y_i + y_{i-1}}{h^2} $$
- Problem $$ \frac{d^2y}{dt^2} = -g $$ with $t \in [0, 5]$, $h = 0.5$, $y_0 = 35$, $y_{10} = 10$.
- How to get $v_0$?
ivp
- It requires both $y_0$ and $v_0$
- Equation $$ y_{i+1} = y_i + h \frac{dy}{dx} $$
- Smaller $h$ gives better result, but it might be no efficient.