pdesolve

pdesolve is a symbolic PDE toolbox built on SymPy. pdesolve(...) is the main solving entry point; the package also exposes focused APIs for first-order PDEs, complete integrals, conservation laws, constant-coefficient operators, transforms/separation, hyperbolic systems, and Green/fundamental solutions.

Quick start

import sympy as sp
import pdesolve as pds

x, t = sp.symbols("x t", real=True)
u = sp.Function("u")
eq = sp.Eq(sp.diff(u(x, t), t) + sp.diff(u(x, t), x), 0)

res = pds.pdesolve(eq, u(x, t), (x, t), method="auto")
print(res.method)
print(res.solution)

PDESolve documentation

The documentation is built from the package API, canonical execution registry, recognizers, planners, regression tests, worked examples, and executable tutorials. Start at docs/index.md. In particular:

• docs/capability-matrix.md — supported PDE families and support level
• docs/method-inventory.md — exact canonical method keys, recognizers, direct APIs, and formal methods
• docs/public-api-inventory.md — all package-level exports and signatures
• docs/inputs-conditions-domains.md — structured inputs and geometry
• docs/results-verification.md — result classes and verification semantics
• docs/planning-diagnostics.md — recognition/ranking/trace inspection
• docs/limitations.md — support boundaries and partial/formal capabilities
• docs/developer-guide.md — extending the package safely
• docs/tutorial-notebooks.md — PDESolve documentation executable tutorial curriculum

A mkdocs.yml navigation file is included so the Markdown tree can be rendered with MkDocs if desired.

Inspecting automatic planning

problem = pds.build_pde_problem(eq, u(x, t), (x, t))
plan = pds.plan_canonical_problem(problem)
for step in plan.steps:
    print(step.method, step.score, step.reasons)

Kernel and Green-function APIs

Use solve_fundamental_solution(...) and solve_green_function(...) for explicit kernel work. Automatic kernel routing is conservative and is primarily source-driven, so ordinary homogeneous heat/wave IVPs continue to use condition-aware IVP, transform, or series paths.

Installation

pip install -e .

Requires Python 3.11+ and SymPy 1.12+.

Tests

python -m pytest -q

The suite covers solver families, coordinator layers, structured conditions/domains, verification/trace behavior, benchmarks, Green functions, and a 52-example heterogeneous PDE reference matrix.

License and source

PDESolve is licensed under the GNU General Public License v3.0 only (GPL-3.0-only). The canonical source repository is https://github.com/BhuvaneshBhatt/pdesolve.

Example materials

Runnable examples include examples/first_order_nonlinear_demo.py, examples/conservation_law_demo.py, examples/invariant_reduction_demo.py, examples/complete_integral_methods.py, and examples/pdesolve_demo.py. Focused notebooks include notebooks/invariant_reduction_demo.ipynb; the systematic tutorial curriculum is under notebooks/tutorials/; the capability matrix and method inventory provide the authoritative overview of supported methods.