mallory — system of differential equations

A coupled 2-variable first-order system, plotted as a phase portrait.

Via Numerical.rk4, which was already a vector-state (system) solver -- extending /ode's single-equation solver to two coupled equations dx/dt = f(x,y,t), dy/dt = g(x,y,t) only needed new glue code, not a new numerical method. v1 is fixed at 2 equations/2 variables (the same scope cut SystemSolverPanel made for algebraic systems), with one trajectory from a single initial condition overlaid on a direction field sampled at t0 -- no multi-trajectory overlay, no animation.

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at t = 15.0000: x = 0.5666, y = 1.7067

Fixed points:

  • (0.0000, 0.0000) — Saddle (λ = -1, 1)
  • (1.0000, 1.0000) — Center (λ = -1.4377832258105627e-11+i, -1.4377832258105627e-11-i)