Python implementation of numerical methods and optimization algorithms.
Isosurface visualization in multidimensional space for generalized blind search algorithm
Convergence to global optimum from local minimum on anisotropic function
Wave equation solution animation using finite difference method
1D parabolic equation solution (mixed boundary problem)
Comparison of differential equation solving methods
Data interpolation using cubic splines
Data approximation with discrete least squares method
Nonlinear system solution using Newton's method
- Diffusion and transport equation solvers (Roberts, Gaussian model, Euler, UpWind)
- Explicit and implicit schemes for PDEs
- Crank-Nicolson method for semi-empirical equations
- Approximation: LSM (discrete and integral)
- ODEs/PDEs: Cauchy problems, boundary problems (Thomas algorithm), hyperbolic and parabolic equations, Dirichlet problem for Laplace equation
- Differentiation: Runge 2nd order method
- Nonlinear equations: Newton, simple iteration, dichotomy
- Nonlinear systems: Newton, simple iteration
- Interpolation: Lagrange (equidistant/non-equidistant nodes), Newton, cubic splines
- Integration: rectangles, trapezoids, Simpson
- Extremum search: bisection, Fibonacci, golden section, quadratic/cubic interpolation, scanning
- Multidimensional optimization:
- Gradient method
- Conjugate gradients
- Gauss-Seidel
- Rosenbrock method
- Pairwise probe (classical, stochastic)
- Custom pairwise probe with direction batching
- Random directions
- Blind search
- Random penalty search
- Generalized algorithms for N-dimensional cases
- My modification of pairwise probe: batching N samples with best direction selection
- Algorithms with usage examples + visualization
- 40+ implemented methods
- Pure Python + NumPy/SciPy + Matplotlib
pip install -r requirements.txt