intro 2 fdm & examples

theory Link to heading

• 08-apr-2020 Persamaan diferensial parsial
• 10-apr-2020 Persamaan diferensial parsial dengan spreadsheet

examples Link to heading

• 08-aug-2019 Diffusion Simulation with JS: Writing Your Own ABM Code
• 27-jun-2020 Molecular Dynamics (MD) Method and Agent-Based Model (AMB) in Simulation of Stem Cell Deposition on the Surface with Nanopattern: Simulator Design
• 25-sep-2019 Compaction of two-dimensional system of composite spherical particles under influence of self-gravitation: Between lock-and-key model and tetris-structure
• 21-aug-2019 Head-on collision of two spherical grains with 2-d internal structure
• 09-aug-2019 Simulation of Blood Cell Separation System Based on Inertia and Elasticity using Molecular Dynamics Method (a simulation design)
• 10-jul-2019 Molecular Dynamics Simulation of Floating Spheres Forming Two-Dimensional Hexagonal Close Packed Structure
• 29-jun-2019 Granular buoyant force in a two-dimensional intruder-particles bed system
• 31-oct-2018 Simulation of snake-like swimming system using granular model

bvp with matrix Link to heading

• 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 Link to heading

• 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.

assignment Link to heading

• url https://github.com/dudung/lecture-notes/issues/20