differential-equations

Build, analyze, and solve ODE and PDE models with numerical solvers.

Updated Jan 26, 2026
One-click install
npx skills add https://github.com/SPIRAL-EDWIN/MCM-ICM-2601000 --skill differential-equations
Or copy as Structured Prompt for Agent
Please help me install this Agent Skill.
Skill: differential-equations
Source: https://github.com/SPIRAL-EDWIN/MCM-ICM-2601000/tree/main/.github/skills/differential-equations
Command: npx skills add https://github.com/SPIRAL-EDWIN/MCM-ICM-2601000 --skill differential-equations

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This skill provides a unified framework to build, analyze, and solve differential equation models (ODEs and PDEs), enabling scientists to reason about dynamics, equilibria, and stability with a common interface.

Core Features & Use Cases

  • Unified API: A single ODEModel class to define, solve, analyze, and fit multiple differential equation systems (logistic growth, Lotka-Volterra, SIR, reaction-diffusion, etc.).
  • Analysis Toolkit: Equilibrium search, Jacobian calculation, linear stability classification, phase-plane visualization, and bifurcation exploration.
  • Model Library & Extensions: Pre-built models and templates that can be extended to custom equations and higher dimensions for spatial problems.

Quick Start

Use the differential-equations skill to build a simple LogisticModel, set r=0.5, K=100, initial N=10, and solve from t=0 to 20 to observe growth dynamics.

Frequently Asked Questions about differential-equations

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I analyze ODE equilibria and phase-plane stability for predator-prey models?

To analyze ODE equilibria and phase-plane stability, this framework calculates Jacobian matrices, classifies linear stability, and visualizes dynamics for predator-prey and other differential equation systems through a unified API.

Can I solve reaction-diffusion PDEs and logistic growth ODEs using the same toolkit?

Yes, you can solve reaction-diffusion PDEs and logistic growth ODEs using the same toolkit, which provides a unified model library and reusable API for defining, solving, and analyzing both ordinary and partial differential equations.

What is the best way to estimate parameters for an SIR differential equation model?

The best way to estimate parameters for an SIR differential equation model is using the toolkit's built-in parameter estimation tools, which integrate directly with the numerical solvers to fit model dynamics to observed data.

Does this differential equations framework support custom equations and higher dimensions?

Yes, this differential equations framework supports custom equations and higher dimensions, allowing you to extend pre-built templates like Lotka-Volterra to address spatial problems and complex dynamical systems beyond standard models.

How do I calculate the Jacobian matrix for ODE stability classification?

You calculate the Jacobian matrix for ODE stability classification by using the toolkit's analysis features, which automatically compute the Jacobian at equilibria to classify stability and support bifurcation exploration.