PDE Solver Library

Purpose

Provides numerical methods and solvers for partial differential equations in mathematical modeling and simulation.

Capabilities

• Finite difference schemes (explicit, implicit, Crank-Nicolson)
• Finite element methods (FEM)
• Finite volume methods
• Spectral methods
• Mesh generation and adaptation
• Stability and convergence analysis

Usage Guidelines

1. Method Selection: Choose method based on PDE type and geometry
2. Mesh Quality: Ensure appropriate mesh resolution
3. Stability Analysis: Verify CFL conditions and stability
4. Convergence: Monitor solution convergence with refinement

Tools/Libraries

• FEniCS
• deal.II
• PETSc
• Firedrake