Index

_

__call__() (nodepy.ode_solver.ODESolver method)

A

A_alpha_stability() (nodepy.linear_multistep_method.LinearMultistepMethod method) absolute_monotonicity_radius() (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.runge_kutta_method.RungeKuttaMethod method) accuracy_efficiency() (in module nodepy.runge_kutta_method)

Adams_Bashforth() (in module nodepy.linear_multistep_method) Adams_Moulton() (in module nodepy.linear_multistep_method) AdditiveLinearMultistepMethod (class in nodepy.linear_multistep_method) arw2() (in module nodepy.linear_multistep_method) arw3() (in module nodepy.linear_multistep_method)

B

backward_difference_formula() (in module nodepy.linear_multistep_method)

C

canonical_shu_osher_form() (nodepy.runge_kutta_method.RungeKuttaMethod method) characteristic_polynomials() (nodepy.linear_multistep_method.LinearMultistepMethod method) circle_contractivity_radius() (nodepy.runge_kutta_method.RungeKuttaMethod method)

compose() (in module nodepy.runge_kutta_method) ContinuousExplicitRungeKuttaMethod (class in nodepy.runge_kutta_method) ContinuousRungeKuttaMethod (class in nodepy.runge_kutta_method) ctest() (nodepy.convergence method)

D

DC() (in module nodepy.runge_kutta_method) DC_pair() (in module nodepy.runge_kutta_method) dcweights() (in module nodepy.runge_kutta_method) density() (nodepy.rooted_trees.RootedTree method) detest() (nodepy.ivp method) discrete_adjoint() (in module nodepy.runge_kutta_method)

dj_reduce() (nodepy.runge_kutta_method.RungeKuttaMethod method) Dmap() (in module nodepy.rooted_trees) (nodepy.rooted_trees.RootedTree method) Dmap_str() (in module nodepy.rooted_trees) Dprod() (in module nodepy.rooted_trees) Dprod_str() (in module nodepy.rooted_trees)

E

E_polynomial() (nodepy.runge_kutta_method.RungeKuttaMethod method) effective_order() (nodepy.runge_kutta_method.RungeKuttaMethod method) effective_order_condition_residuals() (nodepy.runge_kutta_method.RungeKuttaMethod method) elementary_weight() (in module nodepy.runge_kutta_method) elementary_weight_str() (in module nodepy.runge_kutta_method) elementary_weight_str_jump() (in module nodepy.runge_kutta_method) elementary_weight_str_matlab() (in module nodepy.runge_kutta_method) elm_ssp2() (in module nodepy.linear_multistep_method) Emap() (in module nodepy.rooted_trees)

Emap_str() (in module nodepy.rooted_trees) embedded_method (nodepy.runge_kutta_method.ExplicitRungeKuttaPair property) error_coefficient() (nodepy.runge_kutta_method.RungeKuttaMethod method) error_coeffs() (nodepy.runge_kutta_method.RungeKuttaMethod method) error_metrics() (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method) (nodepy.runge_kutta_method.RungeKuttaMethod method) ExplicitRungeKuttaMethod (class in nodepy.runge_kutta_method) ExplicitRungeKuttaPair (class in nodepy.runge_kutta_method) extrap() (in module nodepy.runge_kutta_method) extrap_pair() (in module nodepy.runge_kutta_method)

G

Gprod() (in module nodepy.rooted_trees) (nodepy.rooted_trees.RootedTree method)

Gprod_str() (in module nodepy.rooted_trees) (nodepy.rooted_trees.RootedTree method)

I

imaginary_stability_interval() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) internal_stability_plot() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) internal_stability_polynomials() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) is_absolutely_monotonic_poly() (in module nodepy.runge_kutta_method) is_algebraically_stable() (nodepy.runge_kutta_method.RungeKuttaMethod method) is_explicit() (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) (nodepy.runge_kutta_method.RungeKuttaMethod method)

is_FSAL() (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method) (nodepy.runge_kutta_method.RungeKuttaMethod method) is_splittable() (nodepy.runge_kutta_method.RungeKuttaMethod method) is_zero_stable() (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.runge_kutta_method.RungeKuttaMethod method)

L

lamda() (nodepy.rooted_trees.RootedTree method) lamda_str() (nodepy.rooted_trees.RootedTree method) latex() (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.runge_kutta_method.RungeKuttaMethod method) linear_absolute_monotonicity_radius() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) linear_monotonicity_radius() (nodepy.runge_kutta_method.RungeKuttaMethod method) linearly_stable_step_size() (in module nodepy.runge_kutta_method) LinearMultistepMethod (class in nodepy.linear_multistep_method)

list_equivalent_trees() (nodepy.rooted_trees.RootedTree method) list_trees() (in module nodepy.rooted_trees) load_low_storage() (in module nodepy.low_storage_rk) load_LSRK() (in module nodepy.low_storage_rk) load_LSRK_RKOPT() (in module nodepy.low_storage_rk) loadLMM() (in module nodepy.linear_multistep_method) loadRKM() (in module nodepy.runge_kutta_method) lp_perturb() (nodepy.runge_kutta_method.RungeKuttaMethod method)

M

main_method (nodepy.runge_kutta_method.ExplicitRungeKuttaPair property) maximum_internal_amplification() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) Milne_Simpson() (in module nodepy.linear_multistep_method) module nodepy.linear_multistep_method nodepy.low_storage_rk nodepy.rooted_trees nodepy.runge_kutta_method

N

nodepy.linear_multistep_method module nodepy.low_storage_rk module nodepy.rooted_trees module

nodepy.runge_kutta_method module num_seq_dep_stages() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) Nystrom() (in module nodepy.linear_multistep_method)

O

optimal_perturbed_splitting() (nodepy.runge_kutta_method.RungeKuttaMethod method) optimal_shu_osher_form() (nodepy.runge_kutta_method.RungeKuttaMethod method) order() (nodepy.linear_multistep_method.AdditiveLinearMultistepMethod method) (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.rooted_trees.RootedTree method) (nodepy.runge_kutta_method.RungeKuttaMethod method)

order_condition_residuals() (nodepy.runge_kutta_method.RungeKuttaMethod method)

P

p (nodepy.linear_multistep_method.LinearMultistepMethod property) (nodepy.runge_kutta_method.RungeKuttaMethod property) plot() (nodepy.rooted_trees.RootedTree method) plot_all_trees() (in module nodepy.rooted_trees) plot_boundary_locus() (nodepy.linear_multistep_method.LinearMultistepMethod method) plot_I_controller_stability() (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method) plot_imex_stability_region() (nodepy.linear_multistep_method.AdditiveLinearMultistepMethod method) plot_order_star() (nodepy.runge_kutta_method.RungeKuttaMethod method) plot_PI_controller_stability() (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method) plot_PID_controller_stability() (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method)

plot_stability_function() (nodepy.runge_kutta_method.RungeKuttaMethod method) plot_stability_region() (nodepy.linear_multistep_method.LinearMultistepMethod method) (nodepy.runge_kutta_method.ExplicitRungeKuttaPair method) (nodepy.runge_kutta_method.RungeKuttaMethod method) principal_error_norm() (nodepy.runge_kutta_method.RungeKuttaMethod method) print_shu_osher() (nodepy.runge_kutta_method.RungeKuttaMethod method) propagation_matrix() (nodepy.runge_kutta_method.RungeKuttaMethod method) ptest() (nodepy.convergence method) py2tex() (in module nodepy.rooted_trees) python_to_fortran() (in module nodepy.runge_kutta_method) python_to_matlab() (in module nodepy.runge_kutta_method)

R

real_stability_interval() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method) recursiveVectors() (in module nodepy.rooted_trees) redistribute_gamma() (in module nodepy.runge_kutta_method) relative_accuracy_efficiency() (in module nodepy.runge_kutta_method) resplit() (nodepy.runge_kutta_method.RungeKuttaMethod method) RK22_family() (in module nodepy.runge_kutta_method) RK44_family() (in module nodepy.runge_kutta_method)

RKC1() (in module nodepy.runge_kutta_method) RKC2() (in module nodepy.runge_kutta_method) RKeta() (in module nodepy.runge_kutta_method) RKeta_str() (in module nodepy.runge_kutta_method) RKOCstr2code() (in module nodepy.runge_kutta_method) RootedTree (class in nodepy.rooted_trees) runge_kutta_order_conditions() (in module nodepy.runge_kutta_method) RungeKuttaMethod (class in nodepy.runge_kutta_method)

S

sand_cc() (in module nodepy.linear_multistep_method) shu_osher_change_alpha_ij() (in module nodepy.runge_kutta_method) shu_osher_to_butcher() (in module nodepy.runge_kutta_method) shu_osher_zero_alpha_ij() (in module nodepy.runge_kutta_method) shu_osher_zero_beta_ij() (in module nodepy.runge_kutta_method) sign_split() (in module nodepy.runge_kutta_method) ssp_coefficient() (nodepy.linear_multistep_method.LinearMultistepMethod method) SSPIRK1() (in module nodepy.runge_kutta_method) SSPIRK2() (in module nodepy.runge_kutta_method)

SSPIRK3() (in module nodepy.runge_kutta_method) ssplit() (nodepy.runge_kutta_method.RungeKuttaMethod method) SSPRK2() (in module nodepy.runge_kutta_method) SSPRK3() (in module nodepy.runge_kutta_method) SSPRKm() (in module nodepy.runge_kutta_method) stability_function() (nodepy.runge_kutta_method.RungeKuttaMethod method) stability_function_unexpanded() (nodepy.runge_kutta_method.RungeKuttaMethod method) stage_order() (nodepy.runge_kutta_method.RungeKuttaMethod method) stiff_damping_factor() (nodepy.linear_multistep_method.AdditiveLinearMultistepMethod method) symmetry() (nodepy.rooted_trees.RootedTree method)

T

TwoNRungeKuttaMethod (class in nodepy.low_storage_rk) twoR2butcher() (in module nodepy.low_storage_rk) TwoRRungeKuttaMethod (class in nodepy.low_storage_rk)

TwoRRungeKuttaPair (class in nodepy.low_storage_rk) TwoSRungeKuttaMethod (class in nodepy.low_storage_rk) TwoSRungeKuttaPair (class in nodepy.low_storage_rk) TwoStepRungeKuttaMethod (class in nodepy.twostep_runge_kutta_method)

W

work_per_step() (nodepy.runge_kutta_method.ExplicitRungeKuttaMethod method)