PdeSolver 1.0.0

PdeSolver

A .NET library for solving 1D parabolic partial differential equations using the Crank-Nicolson finite difference method.

PDE Form

The solver handles PDEs of the form:

$$u_t = a(t,x), u_{xx} + b(t,x), u_x + c(t,x), u + f(t,x)$$

where:

• a(t,x) — diffusion coefficient
• b(t,x) — advection coefficient
• c(t,x) — reaction coefficient
• f(t,x) — source term

Installation

dotnet add package PdeSolver

Quick Start

using PdeSolver;

// Define domain: x in [0,1], t in [0,0.1]
var domain = new Domain1D(0.0, 1.0, 0.0, 0.1);

// Create grid: 101 spatial points, 1000 time steps
var grid = new Grid1D(domain, 101, 1000);

// Define PDE (heat equation with sin(πx) initial condition)
var pde = new Pde1D
{
    Diffusion    = (t, x) => 1.0,
    Initial      = (t, x) => Math.Sin(Math.PI * x),
    BoundaryLeft  = (t, x) => 0.0,
    BoundaryRight = (t, x) => 0.0
};

// Solve
var solver = PdeSolverFactory.CreateSolver1D(grid, pde);
double[] solution = solver.Solve();

Features

• Crank-Nicolson scheme — second-order accurate in both time and space
• Configurable theta parameter — set solver.Theta to 0.0 (explicit), 0.5 (Crank-Nicolson), or 1.0 (implicit)
• Flexible coefficients — diffusion, advection, reaction, and source can be functions of (t, x)
• Dirichlet boundary conditions — left and right boundary values as functions of (t, x)
• NuGet-ready — packaged for distribution via NuGet

API Reference

Core Types

Solver

Examples

See the examples project for complete working examples:

1. Heat equation — with exact solution comparison
2. Advection-diffusion — Gaussian bump transport
3. Reaction-diffusion with source — approach to steady state

Building

# Restore and build
dotnet build

# Run tests
dotnet test

# Run examples
dotnet run --project examples/PdeSolver.Examples

# Create NuGet package
dotnet pack src/PdeSolver -c Release

Project Structure

PdeSolver/
├── PdeSolver.sln
├── src/
│   └── PdeSolver/              # Class library (NuGet package)
│       ├── BoundaryType.cs
│       ├── BoundaryConfig1D.cs
│       ├── CoefficientFunction.cs
│       ├── Domain1D.cs
│       ├── Grid1D.cs
│       ├── Pde1D.cs
│       ├── PdeSolverFactory.cs
│       ├── TridiagonalSolver.cs
│       └── Schemes/
│           └── CrankNicolsonSolver1D.cs
├── tests/
│   └── PdeSolver.Tests/        # xUnit test project
└── examples/
    └── PdeSolver.Examples/     # Console demo app

License

MIT