Two-step Runge-Kutta methods

Two-step Runge-Kutta methods are a class of multi-stage multistep methods that use two steps and (potentially) several stages.

class nodepy.twostep_runge_kutta_method.TwoStepRungeKuttaMethod(d, theta, A, b, Ahat=None, bhat=None, type='General', name='Two-step Runge-Kutta Method')[source]

General class for Two-step Runge-Kutta Methods The representation uses the form and partly the notation of [JT95], equation (1.3).

\[\begin{split}\begin{align*} y^n_j = & d_j u^{n-1} + (1-d_j)u^n + \Delta t \sum_{k=1}^{s} (\hat{a}_{jk} f(y_k^{n-1}) + a_{jk} f(y_k^n)) & (1 \le j \le s) \\ u^{n+1} = & \theta u^{n-1} + (1 - \theta)u^n + \Delta t \sum_{j=1}^{s}(\hat{b}_j f(y_j^{n-1}) + b_j f(y_j^n)) \end{align*}\end{split}\]

Initialize a 2-step Runge-Kutta method.