PDEngine Documentation

Welcome to the PDEngine Library documentation! This library provides numerical methods for solving partial differential equations (PDEs) using Julia. Below you will find descriptions of the available functions, methods for solving heat equations and Navier-Stokes equations, and instructions for usage.

Table of Contents

• Getting Started
• Heat Equation Solver
• Navier-Stokes Solver
• Poisson's Equation Solvers
• Wave Equation Solvers
• Manual
• Reference

Getting Started

To use the PDE Library, include the package in your Julia environment. You can then call the functions provided to solve various PDEs.

Heat Equation Solver

The heat equation solver includes methods for solving the 1D heat equation using:

• Finite Difference Method (FDM)
• Finite Element Method (FEM)
• Crank-Nicolson Method (CN)

Navier-Stokes Solver

The Navier-Stokes solver provides methods to solve the 2D Navier-Stokes equations for incompressible flow.

Poisson's Equation Solvers

The Poisson's equation solvers include methods for solving the 2D Poisson's equation using:

• Finite Difference Method (FDM)
• Finite Element Method (FEM)

Wave Equation Solvers

The wave equation solvers include methods for solving the 1D wave equation using:

• Finite Difference Method (FDM)
• Finite Element Method (FEM)

Manual

For detailed instructions on how to use the functions and examples, refer to the Manual.

Reference

For detailed API documentation, refer to the Reference.