findiff

A Python package for finite difference numerical derivatives and partial differential equations in any number of dimensions.

Features

• Differentiate arrays of any number of dimensions along any axis with any desired accuracy order

• Accurate treatment of grid boundary

• Includes standard operators from vector calculus like gradient, divergence and curl

• Can handle uniform and non-uniform grids

• Can handle arbitrary linear combinations of derivatives with constant and variable coefficients

• Fully vectorized for speed

• GPU / JAX / CuPy support for operator application — combine with jax.jit for acceleration

• Calculate raw finite difference coefficients for any order and accuracy

• Generate matrix representations of arbitrary linear differential operators

• Solve partial differential equations with Dirichlet, Neumann or Robin boundary conditions

• Solve eigenvalue problems (e.g. Schrodinger equation, vibration modes)

• Generate differential operators for arbitrary stencils

• Symbolic representation of finite difference schemes

• Periodic boundary conditions for differential operators and PDEs

• Compact (implicit) finite differences with spectral-like resolution

• Estimate truncation error by comparing accuracy orders

• Solve time-dependent PDEs with the Method of Lines (Forward Euler, RK4, Backward Euler, Crank-Nicolson), including wave equations (Stoermer-Verlet), time-dependent boundary values and source terms

Added in version 0.11: Comfortable new API via Diff (the old FinDiff API remains available)

Added in version 0.12: Periodic boundary conditions for differential operators and PDEs

Added in version 0.13: Compact (implicit) finite differences with spectral-like resolution

Added in version 0.14: Time-dependent PDE solving via Method of Lines, GPU / JAX / CuPy backend support for operator application, eigenvalue problems, iterative solvers, Robin boundary conditions and error estimation via accuracy order comparison

Added in version 0.15: Compact finite differences on non-uniform grids, optimal and spectral-like compact schemes

Added in version 0.16: Wave equations (second order in time), time-dependent boundary values and source terms for time-dependent PDEs, stable boundary treatment for high-order operators, much faster implicit time stepping

Content

• Getting Started
  • Installation
  • Taking Derivatives
  • Finite Difference Coefficients
  • Matrix Representations
  • Stencils
  • Legacy API
• Guides
  • Basic Derivatives
  • Vector Calculus
  • Non-Uniform Grids
  • Polar Coordinates
  • Periodic Boundary Conditions
  • Matrix Representation
  • Compact Finite Differences
  • Solving Partial Differential Equations
  • Time-Dependent PDEs
  • Boundary Conditions
  • Error Estimation
  • GPU / JAX / CuPy
  • PDE Cookbook
• Examples
  • Basic Usage
  • Non-Uniform Grids
  • Periodic Boundary Conditions
  • Polar Coordinates
  • Stencils
  • Vector Calculus
  • Symbolic Representation
• Theory
  • Notation
  • The 1D Case
  • Multiple Dimensions
  • Non-Uniform Grids
  • Compact (Implicit) Finite Differences
  • Error Estimation
• API Reference
  • Differential Operators
  • Finite Difference Coefficients
  • Stencils
  • Partial Differential Equations
  • Time-Dependent PDEs
  • Compact Finite Differences
  • Vector Calculus
  • Symbolic
• Migrating from FinDiff to Diff
  • Basic Derivatives
  • Mixed Partial Derivatives
  • Accuracy Control
  • Coefficient and Identity
  • Operator Arithmetic
  • Lazy Grid Setting
  • Matrix Representation
  • Suppressing the Deprecation Warning
• Citing findiff

Indices and tables

• Index

• Module Index

• Search Page