rk_module_variable_step Module

maximum allowed step size

minimum allowed step size

minimum allowed factor for decreasing step size after rejected step

maximum allowed factor for increasing step size after accepted step

method to determine if step is accepted [1,2]

maximum number of attempts to decrease step size before giving up

to use tol*h in the hfactor equation

for hfactor equation (>0)

p + this value in the exponent (0 or 1)

routine for computing the norm of the state

user specified number of variables

user-specified derivative function

user-specified report function

event function (stop when this is zero)

the method for varying the step size

relative tolerance (size(n))

absolute tolerance (size(n))

order of the method

if automatically computing the inital step size, which method to use. 1 = hstart, 2 = hinit.

number of rejected steps

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

the step routine for the rk method

returns p, the order of the method

for automatically computing the initial step size [this is from DDEABM]

for automatically computing the initial step size [this is from DOP853]

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

initialize the class (set n,f, and report)

destructor

main integration routine

integration with event finding

dimension(n)

posneg = sign(1.0_wp,xend-x)

dimension(n)

minimum allowed step size (>0)

maximum allowed step size (>0)

minimum allowed factor for decreasing step size after rejected step (>0)

maximum allowed factor for decreasing step size after accepted step (>0)

the user-specified $||x||$ function

method to determine if step is accepted [1,2]

to use tol*h in the hfactor equation

for hfactor equation (>0)

p + this value in the exponent (0 or 1)

max step size change attempts after rejected step

current step size (<>0)

abs error tolerance (>0)

truncation error estimate (>0)

order of the method

new step size (<>0)

if the step is accepted

number of equations

derivative function

relative tolerance (if size=1, then same tol used for all equations)

absolute tolerance (if size=1, then same tol used for all equations)

method for varying the step size

which method to use for automatic initial step size computation. 1 = use hstart, 2 = use hinit.

for reporting the steps

for stopping at an event

initial time

initial state

initial abs(time step)

final time

final state

0 = no errors, <0 = error. if not present, an error will stop program.

initial time

initial state

abs(time step)

max final time if event not located

function tolerance for root finding

actual final time reached

final state (at tf)

g value at tf

0 = no errors, <0 = error. if not present, an error will stop program.

initial time

initial state

time step

state at time t+h

truncation error estimate

initial time

initial state

time step

state at time t+h

truncation error estimate

initial time

initial state

time step

state at time t+h

truncation error estimate

initial time

initial state

time step

state at time t+h

truncation error estimate

initial time

initial state

time step

state at time t+h

truncation error estimate

the initial point of integration.

a value of the independent variable used to define the direction of integration. a reasonable choice is to set b to the first point at which a solution is desired. you can also use b, if necessary, to restrict the length of the first integration step because the algorithm will not compute a starting step length which is bigger than abs(b-a), unless b has been chosen too close to a. (it is presumed that hstart has been called with b different from a on the machine being used. also see the discussion about the parameter small.)

the vector of initial values of the neq solution components at the initial point a.

the vector of derivatives of the neq solution components at the initial point a. (defined by the differential equations in subroutine me%f)

the vector of error tolerances corresponding to the neq solution components. it is assumed that all elements are positive. following the first integration step, the tolerances are expected to be used by the integrator in an error test which roughly requires that abs(local error) <= etol for each vector component.

appropriate starting step size to be attempted by the differential equation method.