Iterative numerical methods for linear systems, spectral collocation, numerical examples, convergence, Numerical computation of matrix norms, conditioning, scaling, pseudospectral method, Linear first-order PDEs, dynamical systems, Preconditioners, fast Fourier transform, first-order partial differential equations, Newton's method, Numerical bifurcation problems, bifurcation, invariant torus, Spectral, collocation and related methods for boundary value problems involving PDEs, Computational methods for bifurcation problems in dynamical systems, iterative methods for nonsymmetric systems, van der Pol oscillator