index.qmd

# Welcome {.unnumbered}

This book teaches finite difference methods for solving partial differential equations, featuring [Devito](https://www.devitoproject.org/) for high-performance PDE solvers.

::: {.content-visible when-format="html"}
[**Download PDF version**](Finite-Difference-Computing-with-PDEs.pdf){.btn .btn-primary}
:::

## About this Edition {.unnumbered}

This edition is based on *[Finite Difference Computing with PDEs: A Modern Software Approach](https://doi.org/10.1007/978-3-319-55456-3)* by Hans Petter Langtangen and Svein Linge (Springer, 2017). This Devito edition features:

- **[Devito](https://www.devitoproject.org/)** - A domain-specific language for symbolic PDE specification and automatic code generation
- **[Quarto](https://quarto.org/)** - Modern scientific publishing for web and PDF output
- **Modern Python** - Type hints, testing, and CI/CD practices

## License {.unnumbered}

::: {.content-visible when-format="html"}
[![CC BY 4.0](https://img.shields.io/badge/License-CC%20BY%204.0-lightgrey.svg)](https://creativecommons.org/licenses/by/4.0/)
:::

This work is licensed under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/), the same license as the original work.

## What is Devito? {.unnumbered}

Devito allows you to write PDEs symbolically and automatically generates optimized finite difference code:

```python
from devito import Grid, TimeFunction, Eq, Operator, solve, Constant

grid = Grid(shape=(101,), extent=(1.0,))
u = TimeFunction(name='u', grid=grid, time_order=2, space_order=2)
c = Constant(name='c')  # wave speed

# Write the wave equation symbolically: u_tt = c^2 * u_xx
pde = Eq(u.dt2, c**2 * u.dx2)

# Solve for u at the next time step
update = Eq(u.forward, solve(pde, u.forward))

# Devito generates optimized C code
op = Operator([update])
op.apply(time_M=100, dt=0.001, c=1.0)
```

## Book Structure {.unnumbered}

The book covers:

1. **Introduction to Devito** - Grid, Function, TimeFunction, Operator, and boundary conditions
2. **Wave Equations** - 1D/2D wave propagation, sources, absorbing boundaries
3. **Diffusion Equations** - Heat equation, stability analysis, 2D extension
4. **Advection Equations** - Upwind schemes, Lax-Wendroff, CFL condition
5. **Nonlinear Problems** - Operator splitting, Burgers' equation, Picard iteration

Plus appendices on finite difference formulas, truncation error analysis, and software engineering.

## Getting Started {.unnumbered}

```bash
git clone https://github.com/devitocodes/devito_book.git
cd devito_book
pip install -e ".[devito]"
```

See the [GitHub repository](https://github.com/devitocodes/devito_book) for full installation instructions.