// Use when solving ordinary or partial differential equations numerically, including choosing integrators, discretization schemes, and stability analysis.
| name | numerical_ode_pde |
| description | Use when solving ordinary or partial differential equations numerically, including choosing integrators, discretization schemes, and stability analysis. |
Apply this skill when equations of motion, field equations, or other differential equations must be solved numerically, and you need to choose appropriate algorithms, set up discretization, and control numerical errors.
Solve differential equations numerically with controlled accuracy, choosing appropriate methods for the problem type (stiff/non-stiff, initial/boundary value, elliptic/parabolic/hyperbolic).
equations: The differential equations in explicit or implicit formdomain: Spatial and/or temporal domain with boundary/initial conditionsparameters: Physical constants, coupling strengths, etc.accuracy_target: Desired relative/absolute tolerance or grid resolutionmethod_choice: The recommended numerical method with justificationdiscretization: Grid/step-size setup, including adaptive criteria if applicablesolution_code: Python code implementing the numerical solution (using scipy, numpy, or manual implementation)stability_check: CFL condition, stiffness assessment, or energy drift analysisClassify the problem.
Choose the numerical method.
Set up the discretization.
Implement and solve.
Validate.
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