Equation Solver Agent

WHAT IT DOES

Three-approach solver for differential equations and systems. First attempts symbolic solution via code generation — writes SymPy code to solve analytically, with self-debugging loop if execution fails. If symbolic intractable, falls back to numerical methods (finite difference, spectral, Runge-Kutta) with convergence analysis. For boundary value problems and PDE systems, generates complete solver code, validates against known solutions, and iterates with self-refinement. Every solution includes: step-by-step derivation, LaTeX rendering, verification (substitution check or numerical convergence proof), and solution visualisation (phase portraits for ODEs, surface plots for PDEs). Handles: linear/nonlinear ODEs, systems of ODEs, PDEs (elliptic, parabolic, hyperbolic), eigenvalue problems, stability analysis.

WORKFLOW

1. Parse equation
2. Classify type (ODE/PDE, order, linearity)
3. Attempt symbolic (SymPy code gen + self-debug)
4. If intractable: numerical (finite diff/spectral/RK4)
5. Verify solution (substitution or convergence)
6. Render LaTeX + plots
7. Show full derivation steps

SKILLS

INTEGRATIONS