VIASM Codes for Summer School on ANM 2025

Hands-on codes for VIASM 2025 summer school on advanced numerical methods for deterministic and stochastic differential equations.

The lectures that introduce and motivate these codes are available on Google Drive: https://tinyurl.com/viasm-anm2025.

Setup

These codes require a modern Python installation, a few standard Python modules, and the git command for interacting with GitHub. The following step-by-step instructions guide you in installing Anaconda, downloading code from GitHub, and running the code in Spyder. These steps are suitable for both Windows and MacOS users.

Install Anaconda

For Windows & macOS

1. Go to the Anaconda website:

   https://www.anaconda.com/download

2. Download the Installer:

   • Click Download

   • Choose the version for your operating system (Windows or MacOS).

   • Download the 64-bit Graphical Installer.

3. Install Anaconda:

   • Windows: Double-click the .exe file and follow the setup instructions.

   • Mac: Double-click the .pkg file and follow the prompts.

   Tip: Leave all settings at their defaults unless you have specific needs. On Windows, you may want to check "Add Anaconda to my PATH environment variable" (optional but useful).

Launch Anaconda Navigator

Open Anaconda Navigator from your Start Menu (Windows) or Applications folder (MacOS).

Download Code from GitHub

Option 1: Using Git (Recommended)

1. Install Git (if you don't have this already):

   Download from https://git-scm.com/downloads and install using default settings.

2. Open Anaconda Prompt (Windows) or Terminal (Mac).

3. Navigate to the folder where you want to save the code:

   cd path/to/your/folder

   where you replace path/to/your/folder with the path to your desired folder.

4. Clone the repository:

   git clone https://github.com/drreynolds/viasm.git

Option 2: Download ZIP (No Git Required)

1. Go to the GitHub repository page in your web browser.

2. Click the green Code button, then select Download ZIP.

3. Extract the ZIP file to your preferred location.

Installing Python dependencies

To install the Python packages that are used by the codes in this repository, use Anaconda Prompt/Terminal from the folder containing the downloaded/cloned code:

pip install -r python_requirements.txt

Running the codes

Option 1: run directly in Anaconda Prompt/Terminal

Run the desired Python script directly at the command-line:

python scriptname.py

where scriptname.py is the name of the script you wish to run.

Option 2: run in Spyder

1. Launch Spyder:

   • In Anaconda Navigator, locate Spyder.

   • If not already installed, click Install.

   • After installation, click Launch to open Spyder.

2. Open and run the code in Spyder

   1. In Spyder, go to File > Open.

   2. Navigate to the folder containing the downloaded/cloned code.

   3. Select the .py file you want to run and open it.

   4. Press the green Run button (Play icon) in Spyder to execute your script.

File layout

Files that begin with capital letters contain Python classes and user-callable functions. Files that begin with lower-case letters contain scripts that run various demos. These are grouped as follows:

Background

Basic Python demos:

• numpy_demo.py -- simple script showing Numpy usage.

• plotting_demo.py -- simple script showing how to generate plots.

Fixed-step Runge--Kutta methods and implicit solvers

• ForwardEuler.py -- simple baseline explicit IVP time-stepper class.

• ERK.py -- explicit Runge--Kutta IVP time-stepper class.

• driver_explicit_fixed.py -- script to test explicit fixed-step methods.

• driver_explicit_stability.py -- script to demonstrate stability limitations of explicit methods.

• ImplicitSolver.py -- reusable nonlinear solver class for implicit IVP methods.

• BackwardEuler.py -- simple baseline implicit IVP time-stepper class.

• DIRK.py -- diagonally-implicit Runge--Kutta IVP time-stepper class.

• driver_implicit_fixed.py -- script to test implicit fixed-step methods.

Adaptive-step Runge--Kutta methods

• AdaptERK.py -- explicit Runge--Kutta adaptive IVP solver class.

• driver_explicit_adaptive.py -- script to test explicit adaptive-step methods.

• AdaptDIRK.py -- implicit Runge--Kutta adaptive IVP solver class.

• driver_implicit_adaptive.py -- script to test implicit adaptive-step methods.

• driver_adaptive_timescale.py -- script to demonstrate how adaptive solvers track dynamical time scales.

• driver_adaptive_stability.py -- script to demonstrate how adaptive solvers can assess stiffness.

Multirate methods

• LTSubcycling.py -- simple fixed-step Lie--Trotter subcycling IVP time-stepper class.

• SMSubcycling.py -- simple fixed-step Strang--Marchuk subcycling IVP time-stepper class.

• MRI.py -- higher-order fixed-step multirate infinitesimal (MRI) IVP time-stepper class.

• driver_multirate.py -- script to demonstrate accuracy differences for various multirate methods.

Auxiliary utilities

• RK_stability.py -- function to plot linear stability regions for Runge--Kutta methods.

Authors

Daniel R. Reynolds
Mathematics & Statistics @ UMBC

Van Hoang Nguyen
Mathematics & Statistics @ TTU