GitHub

PositiveIntegrators.jl API

RKOpt.optimize_stability_polynomial — Method
optimize_stability_polynomial(accuracy_order,
                              number_of_stages,
                              spectrum;
                              dt_min = 0.0,
                              dt_max = 2.01 * number_of_stages^2 *
                                       maximum(abs, spectrum),
                              tol_bisect = 1.0e-9,
                              tol_feasible = 1.0e-9,
                              maxiters = 1000,
                              optimizer = ECOS.Optimizer,
                              silent = true)

Optimize the stability polynomial of an explicit Runge-Kutta method with a given accuracy_order and number_of_stages for a given spectrum of eigenvalues (a vector of real or complex numbers) using the algorithm of Ketcheson and Ahmadia (2012).

Optional keyword arguments

  • dt_min = 0.0: Minimum time step size for the bisection.
  • dt_max = 2.01 * number_of_stages^2 * maximum(abs, spectrum): Maximum time step size for the bisection.
  • tol_bisect = 1.0e-9: Relative tolerance used to terminate the bisection.
  • tol_feasible = 1.0e-9: Relative tolerance used to determine the feasibility of the optimization. The problem is considered feasible if the maximal absolute value of the stability polynomial is less than or equal to 1 + tol_feasible at all eigenvalues in the spectrum.
  • maxiters = 1000: Maximum number of iterations for the bisection.
  • optimizer = ECOS.Optimizer: Convex optimization solver to be used. You can choose a solver supporting SOCP from the list of supported solvers in the JuMP documentation.
  • silent = true: Whether to suppress the output of the convex optimization solver.

References

source