Select and configure time integration methods for ODE/PDE simulations. Use when choosing explicit/implicit schemes, setting error tolerances, adapting time steps, or diagnosing integration accuracy and stability issues.
This Claude skill provides a specialized toolkit for managing numerical integration in scientific computing. It automates the complex decision-making process for ODE and PDE simulations, including integrator selection, adaptive time-stepping, and stiffness handling. By offering a structured workflow and Python-based utilities, it helps developers and researchers ensure the stability, accuracy, and efficiency of time-dependent mathematical models.
Use Cases
Automated Integrator Selection: Choosing between explicit schemes like RK45 for non-stiff problems and implicit methods like BDF or Rosenbrock for stiff systems based on Jacobian availability.
Adaptive Time-Step Management: Implementing PI or PID controllers to dynamically adjust simulation time steps, maintaining user-defined error tolerances while optimizing computational performance.
Stiff System Diagnosis: Identifying stiffness in coupled systems and determining whether to switch from explicit to implicit solvers to prevent numerical instability.
IMEX Splitting Strategy: Planning Implicit-Explicit (IMEX) splitting for complex physics models, such as diffusion-reaction equations, to handle different terms with the most appropriate numerical methods.
Error Norm Validation: Computing scaled error norms and performing convergence checks to verify the reliability of simulation results under various tolerance settings.
name
numerical-integration
description
Select and configure time integration methods for ODE/PDE simulations. Use when choosing explicit/implicit schemes, setting error tolerances, adapting time steps, diagnosing integration accuracy, planning IMEX splitting, or handling stiff/non-stiff coupled systems.
allowed-tools
Read, Bash, Write, Grep, Glob
Numerical Integration
Goal
Provide a reliable workflow to select integrators, set tolerances, and manage adaptive time stepping for time-dependent simulations.
Requirements
Python 3.8+
NumPy (for some scripts)
No heavy dependencies for core functionality
Inputs to Gather
Input
Description
Example
Problem type
ODE/PDE, stiff/non-stiff
stiff PDE
Jacobian available
Can compute ∂f/∂u?
yes
Target accuracy
Desired error level
1e-6
Constraints
Memory, implicit allowed?
implicit OK
Time scale
Characteristic time
1e-3 s
Decision Guidance
Choosing an Integrator
Is the problem stiff?
├── YES → Is Jacobian available?
│ ├── YES → Use Rosenbrock or BDF
│ └── NO → Use BDF with numerical Jacobian
└── NO → Is high accuracy needed?
├── YES → Use RK45 or DOP853
└── NO → Use RK4 or Adams-Bashforth
