Numerical Methods for Partial Differential Equations Package

This package provides multiple numerical routines for solving partial differential equations, including implementations of the Lax-Friedrichs method for first-order accuracy with artificial viscosity, the Lax-Wendroff scheme offering second-order accuracy for hyperbolic equations, and various upwind schemes that handle directional dependence in convection-dominated problems. Users can customize simulation parameters such as time step size (Δt) and spatial grid resolution (Δx) to balance computational accuracy and efficiency. The modular design allows for easy extension through additional boundary condition handlers or modification of existing solver components. Each routine includes configurable Courant-Friedrichs-Lewy (CFL) condition checks to ensure numerical stability. The package architecture supports flexible integration with user-defined initial conditions and source terms through callback functions. Key features include vectorized operations for performance optimization and visualization hooks for result analysis. This provides a versatile, extensible platform addressing diverse PDE numerical solving requirements across scientific computing applications.