PySolverKit

A compact Python library that brings classical numerical methods to life — root finding, interpolation, differentiation, integration, ODE solvers, linear systems, and 2D FEM for Poisson problems.

Features

• Function arithmetic — add, subtract, multiply, and compose built-in function types (Polynomial, Sin, Cos, Tan, Exponent, Log) with plain Python operators
• Root finding — bisection, Newton-Raphson, secant, Regula Falsi, and modified Newton methods
• Interpolation — Lagrange and Newton divided-difference forms (forward/backward difference tables included)
• Differentiation — forward, backward, and central finite-difference schemes; set an exact derivative for Newton-type solvers
• Integration — rectangular, midpoint, trapezoidal, Simpson's, and Gauss-Legendre quadrature
• ODE solvers — Euler, Runge-Kutta (orders 1–4), Taylor series, trapezoidal, Adams-Bashforth/Moulton, and predictor-corrector methods for first-order IVPs; shooting and finite-difference methods for second-order BVPs
• Linear algebra — Vector and Matrix with arithmetic operations, and LinearSystem with Gaussian elimination and Gauss-Jacobi/Seidel iterative solvers
• 2D FEM — FEM2D for Poisson equations on rectangular domains with Dirichlet boundary conditions

Quick start

import math
from pysolverkit import Polynomial, Sin, RootFindingMethod, IntegrationMethod

# Root finding
f = Polynomial(-6, 14, -7, 1)   # x³ − 7x² + 14x − 6
root = f.root(RootFindingMethod.BISECTION, a=0, b=1, TOLERANCE=1e-6)

# Integration
g = Sin(Polynomial(0, 1))       # sin(x)
area = g.integrate(0, math.pi, method=IntegrationMethod.SIMPSON, n=100)

Documentation

Full API reference, detailed usage examples, and a method selector reference are in docs/README.md.

Running tests

python3 -m unittest discover -s tests -v

Contributing

Contributions are welcome! To get started:

1. Fork the repository and create a feature branch.
2. Add or update tests in tests/tests.py for any new behaviour.
3. Ensure all tests pass: python3 -m unittest discover -s tests -v
4. Open a pull request with a clear description of the change.