Equations Archive
Nonlinear Equation Benchmark Problems
Rosenbrock Function
Famous 'valley' function used as a standard test case for optimization problems.
Powell's Singular Function
A problem where the Jacobian matrix becomes singular, targeting weaknesses in Newton's method.
Broyden Tridiagonal Function
Tridiagonal structure problem for testing large-scale and high-dimensional scalability.
Lorenz Attractor
The gold standard of chaos theory found in weather models. Visualization of the 'Butterfly Effect' from deterministic equations.
Van der Pol Oscillator
Self-excited oscillation equation proposed as a vacuum tube model. Convergence to limit cycles and transition to relaxation oscillations.
Stewart Platform
Forward kinematics of a 6-DOF parallel link mechanism. Numerical solution using SPICE and robust measures against singularities.
Double Pendulum
Double pendulum following Lagrangian mechanics. Visualization of chaotic behavior and verification of numerical accuracy based on energy conservation.
Restricted Three-Body Problem
Search for the 5 equilibrium points (Lagrange points) in the restricted three-body problem (Earth-Moon system).
1D Heat Equation
Numerical simulation of the 1D heat equation. Discretization process and equivalent circuit analysis using SPICE B-sources.
Linear Programming
Analysis of the Klee-Minty problem. Exploration of global optimum using convex formulation with Augmented Lagrangian and Homotopy method applied to KKT conditions.