dedalus.core.timesteppers

ODE integrator classes for timestepping.

Module Contents

class CNAB1(solver)

1st-order Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.5.3]

Implicit: 2nd-order Crank-Nicolson Explicit: 1st-order Adams-Bashforth (forward Euler)

classmethod compute_coefficients(timesteps, iteration)

amax = 1

bmax = 1

cmax = 1

steps = 1

class CNAB2(solver)

2nd-order Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.9]

Implicit: 2nd-order Crank-Nicolson Explicit: 2nd-order Adams-Bashforth

classmethod compute_coefficients(timesteps, iteration)

amax = 2

bmax = 2

cmax = 2

steps = 2

class CNLF2(solver)

2nd-order Crank-Nicolson leap-frog scheme [Wang 2008 eqn 2.11]

Implicit: ?-order wide Crank-Nicolson Explicit: 2nd-order leap-frog

classmethod compute_coefficients(timesteps, iteration)

amax = 2

bmax = 2

cmax = 2

steps = 2

class MCNAB2(solver)

2nd-order modified Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.10]

Implicit: 2nd-order modified Crank-Nicolson Explicit: 2nd-order Adams-Bashforth

classmethod compute_coefficients(timesteps, iteration)

amax = 2

bmax = 2

cmax = 2

steps = 2

class RK111(solver)

1st-order 1-stage DIRK+ERK scheme [Ascher 1997 sec 2.1]

A

H

c

stages = 1

class RK222(solver)

2nd-order 2-stage DIRK+ERK scheme [Ascher 1997 sec 2.6]

A

H

c

stages = 2

γ

δ

class RK443(solver)

3rd-order 4-stage DIRK+ERK scheme [Ascher 1997 sec 2.8]

A

H

c

stages = 4

class RKGFY(solver)

2nd-order 2-stage scheme from Hollerbach and Marti

A

H

c

stages = 2

class RKSMR(solver)

(3-ε)-order 3rd-stage DIRK+ERK scheme [Spalart 1991 Appendix]

A

H

c

stages = 3

class SBDF1(solver)

1st-order semi-implicit BDF scheme [Wang 2008 eqn 2.6]

Implicit: 1st-order BDF (backward Euler) Explicit: 1st-order extrapolation (forward Euler)

classmethod compute_coefficients(timesteps, iteration)

amax = 1

bmax = 1

cmax = 1

steps = 1

class SBDF2(solver)

2nd-order semi-implicit BDF scheme [Wang 2008 eqn 2.8]

Implicit: 2nd-order BDF Explicit: 2nd-order extrapolation

classmethod compute_coefficients(timesteps, iteration)

amax = 2

bmax = 2

cmax = 2

steps = 2

class SBDF3(solver)

3rd-order semi-implicit BDF scheme [Wang 2008 eqn 2.14]

Implicit: 3rd-order BDF Explicit: 3rd-order extrapolation

classmethod compute_coefficients(timesteps, iteration)

amax = 3

bmax = 3

cmax = 3

steps = 3

class SBDF4(solver)

4th-order semi-implicit BDF scheme [Wang 2008 eqn 2.15]

Implicit: 4th-order BDF Explicit: 4th-order extrapolation

classmethod compute_coefficients(timesteps, iteration)

amax = 4

bmax = 4

cmax = 4

steps = 4