Module pde 

Partial Differential Equation (PDE) Solvers

This module provides a comprehensive framework for solving partial differential equations. It includes classification, various solution methods, and support for standard PDEs like heat, wave, and Laplace equations.

Organization

• types: Core PDE types and boundary/initial conditions
• classification: PDE classification algorithms (order, linearity, type)
• registry: Registry-based solver dispatch (O(1) lookup, extensible)
• methods: Solution methods (separation of variables, method of characteristics)
• standard: Standard PDE solvers (heat, wave, Laplace)
• common: Shared utilities for PDE solving

Examples

use mathhook_core::calculus::pde;
use mathhook_core::{symbol, expr};

let u = symbol!(u);
let x = symbol!(x);
let t = symbol!(t);
let equation = expr!(u);
let pde = pde::Pde::new(equation, u, vec![x, t]);

// Solve using automatic solver selection
let solution = pde::solve(&pde).unwrap();

Re-exports

pub use registry::PDEError;

pub use registry::PDEResult;

pub use registry::PDESolver;

pub use registry::PDESolverRegistry;

pub use educational::*;

pub use method_of_characteristics::*;

pub use separation_of_variables::*;

pub use types::*;

Modules

classification

PDE classification algorithms

common

Common utilities for PDE solving

educational

Educational PDE solving with step-by-step explanations

method_of_characteristics

Method of characteristics for first-order PDEs

registry

PDE Solver Registry

separation_of_variables

Separation of variables method for PDEs

standard

Standard PDE Solvers

types

Type definitions for partial differential equations

Functions

solve

Solves a PDE using automatic solver selection.