Numerical Methods Package for Partial Differential Equations

This specialized package is designed for numerical solutions of partial differential equations (PDEs). It incorporates multiple solution methods for key PDE types including Laplace equations, convection equations, and diffusion equations. The implementation features various numerical approaches such as finite difference methods, finite element methods, and spectral methods depending on the equation type and boundary conditions. The package provides extensive parameter configuration options allowing users to customize solver settings, boundary conditions, and convergence criteria. Users can efficiently perform numerical computations through well-documented API calls, with the package handling matrix assembly, iterative solving, and error estimation automatically. The computational core utilizes optimized algorithms for spatial discretization and time integration, ensuring accurate results with controlled computational costs. This versatile package finds applications across multiple disciplines including physics, chemistry, and engineering fields. Future developments will expand functionality with additional equation types, adaptive mesh refinement, and parallel computing capabilities for enhanced precision and performance.