dvode_module Module

weighted r.m.s. norm of accumulated correction vectors.

threshhold on drc for updating the jacobian. (see drc.)

the saved value of tq(5).

estimated corrector convergence rate constant.

relative change in h*rl1 since last dvjac call.

real array of integration coefficients. see dvset.

saved tentative ratio of new to old h.

saved maximum value of eta to be allowed.

the step size.

the minimum absolute value of the step size h to be used.

inverse of the maximum absolute value of h to be used. hmxi = 0.0 is allowed and corresponds to an infinite hmax.

the step size to be attempted on the next step.

step size h used in scaling of nordsieck array yh in dvjust. (if iord = +1, dvjust assumes that hscal = tau(1).) see references 1 and 2 for details.

the saved value of rl1.

ratio of current h*rl1 to value on last dvjac call.

the reciprocal of the coefficient el(1).

real vector of past nq step sizes, length 13.

a real vector of length 5 in which dvset stores constants used for the convergence test, the error test, and the selection of h at a new order.

the independent variable, updated on each step taken.

the machine unit roundoff. the smallest positive real number such that 1.0 + uround /= 1.0

integer flag for convergence failure in dvnlsd:

saved integer flag indicating whether initialization of the problem has been done (init = 1) or not.

saved flag to signal updating of newton matrix.

output flag from dvjac showing jacobian status:

integer flag used as input to dvstep:

integer flag for jacobian saving, = sign(mf).

a completion code from dvstep with the following meanings:

input flag to dvstep showing whether h was reduced by the driver. kuth = 1 if h was reduced, = 0 otherwise.

integer variable, nq + 1, current order plus one.

maxord + 1 (used for dimensioning).

saved integer pointers to segments of rwork and iwork.

saved integer pointers to segments of rwork and iwork.

saved integer pointers to segments of rwork and iwork.

saved integer pointers to segments of rwork and iwork.

saved integer pointers to segments of rwork and iwork.

saved integer pointers to segments of rwork and iwork.

a pointer to the saved jacobian, whose storage starts at wm(locjs), if jsv = 1.

the maximum order of integration method to be allowed.

the method flags. see mf.

the method flags. see mf.

the maximum number of steps between j evaluations, = 50.

saved value of optional input mxhnil.

saved value of optional input mxstep.

the number of first-order odes, = neq.

saved integer to flag change of h.

the method order to be used on the next step.

saved counter for occurrences of t + h = t.

integer variable, the current integration method order.

saved value of nq*nyh.

a counter controlling the frequency of order changes. an order change is about to be considered if nqwait = 1.

the number of steps taken as of the last jacobian update.

saved value of nst as of last newton matrix update.

saved value of the initial value of neq.

the step size in t last used.

number of nonlinear convergence failures so far.

the number of error test failures of the integrator so far.

the number of f evaluations for the problem so far.

the number of jacobian evaluations so far.

the number of matrix lu decompositions so far.

number of nonlinear iterations so far.

the method order last used.

the number of steps taken for the problem so far.

internal data (formerly in common blocks)

logical unit number for messages. the default is obtained by a call to iumach (may be machine-dependent).

print control flag:

this routine must be called first before using the solver.

main solver routine.

set the logical unit number, lun, for output of messages from dvode, if the default is not desired. the default value of lun is output_unit. this call may be made at any time and will take effect immediately.

set a flag to control the printing of messages by dvode:

saves and restores the contents of the internal variables used by dvode. dvsrco is useful if one is interrupting a run and restarting later, or alternating between two or more problems solved with dvode.

provide derivatives of y, of various orders, at a specified point t, if desired. it may be called only after a successful return from dvode.

parameter indicator (1 for lunit, 2 for mesflg).

the value to be set for the parameter, if iset = .true.

logical flag to indicate whether to read or write. if iset = .true., the parameter will be given the value ivalue. if iset = .false., the parameter will be unchanged, and ivalue is a dummy argument.

the name of the user-supplied subroutine defining the ode system. the system must be put in the first-order form dy/dt = f(t,y), where f is a vector-valued function of the scalar t and the vector y. subroutine f is to compute the function f. it is to have the form subroutine f (neq, t, y, ydot) real(wp) t, y(neq), ydot(neq) where neq, t, and y are input, and the array ydot = f(t,y) is output. y and ydot are arrays of length neq. subroutine f should not alter y(1),...,y(neq). f must be declared external in the calling program.

the name of the user-supplied routine (miter = 1 or 4) to compute the jacobian matrix, df/dy, as a function of the scalar t and the vector y. it is to have the form f_jac, where neq, t, y, ml, mu, and nrowpd are input and the array pd is to be loaded with partial derivatives (elements of the jacobian matrix) in the output. pd must be given a first dimension of nrowpd. t and y have the same meaning as in subroutine f.

the following subroutine is called just before each internal integration step, and sets the array of error weights, ewt, as described under itol/rtol/atol above: subroutine dewset (neq, itol, rtol, atol, ycur, ewt) where neq, itol, rtol, and atol are as in the dvode call sequence, ycur contains the current dependent variable vector, and ewt is the array of weights set by dewset.

the following is a real function routine which computes the weighted root-mean-square norm of a vector v: d = dvnorm (n, v, w) where:

the size of the ode system (number of first order ordinary differential equations). neq may not be increased during the problem, but can be decreased (with istate = 3 in the input).

a real array for the vector of dependent variables, of length neq or more. used for both input and output on the first call (istate = 1), and only for output on other calls. on the first call, y must contain the vector of initial values. in the output, y contains the computed solution evaluated at t. if desired, the y array may be used for other purposes between calls to the solver.

the independent variable. in the input, t is used only on the first call, as the initial point of the integration. in the output, after each call, t is the value at which a computed solution y is evaluated (usually the same as tout). on an error return, t is the farthest point reached.

the next value of t at which a computed solution is desired.

an indicator for the type of error control. 1 or 2 according as atol is a scalar or array. see description under atol.

a relative error tolerance parameter, either a scalar or an array of length neq. see description under atol.

an absolute error tolerance parameter, either a scalar or an array of length neq.

an index specifying the task to be performed. input only. itask has the following values and meanings:

an index used for input and output to specify the the state of the calculation.

an integer flag to specify whether or not any optional input is being used on this call. the optional input is listed separately below.

a real working array. the length of rwork must be at least 20 + nyh*(maxord + 1) + 3*neq + lwm where:

the length of the array rwork, as declared by the user. (this will be checked by the solver.)

an integer work array. the length of iwork must be at least:

the length of the array iwork, as declared by the user. (this will be checked by the solver.)

method flag. standard values are:

size of ode system

initial value of independent variable

vector of initial conditions

vector of initial first derivatives

first output value of independent variable

machine unit roundoff

error weights and tolerance parameters as described in the driver routine

error weights and tolerance parameters as described in the driver routine

error weights and tolerance parameters as described in the driver routine

work array of length n

work array of length n

step size to be attempted

number of iterations (and of f evaluations) to compute h0

the error flag, returned with the value:

value of independent variable where answers are desired (normally the same as the t last returned by dvode). for valid results, t must lie between tcur - hu and tcur. (see optional output for tcur and hu.)

integer order of the derivative desired. k must satisfy 0 <= k <= nqcur, where nqcur is the current order (see optional output). the capability corresponding to k = 0, i.e. computing y(t), is already provided by dvode directly. since nqcur >= 1, the first derivative dy/dt is always available with dvindy.

the history array yh

column length of yh, equal to the initial value of neq.

a real array of length neq containing the computed value of the k-th derivative of y(t).

integer flag, returned as 0 if k and t were legal, -1 if k was illegal, and -2 if t was illegal. on an error return, a message is also written.

an array of length n used for the dependent variable vector.

an ldyh by lmax array containing the dependent variables and their approximate scaled derivatives, where lmax = maxord + 1. yh(i,j+1) contains the approximate j-th derivative of y(i), scaled by h**j/factorial(j) (j = 0,1,...,nq). on entry for the first step, the first two columns of yh must be set from the initial values.

a constant integer >= n, the first dimension of yh. n is the number of odes in the system.

a one-dimensional array occupying the same space as yh.

an array of length n containing multiplicative weights for local error measurements. local errors in y(i) are compared to 1.0/ewt(i) in various error tests.

an array of working storage, of length n. also used for input of yh(*,maxord+2) when jstart = -1 and maxord < the current order nq.

a work array of length n passed to subroutine dvnlsd.

a work array of length n, used for the accumulated corrections. on a successful return, acor(i) contains the estimated one-step local error in y(i).

real work array associated with matrix operations in dvnlsd.

integer work array associated with matrix operations in dvnlsd.

leading dimension of yh

an integer flag used when meth = 2 to indicate an order increase (iord = +1) or an order decrease (iord = -1).

the dependent variable, a vector of length n

the nordsieck (taylor) array, ldyh by lmax, input and output. on input, it contains predicted values.

a constant >= n, the first dimension of yh

unused work array.

a work array of length n.

an error weight vector of length n

a work array of length n, used for the accumulated corrections to the predicted y vector.

integer work array associated with matrix operations in chord iteration (miter /= 0).

real work array associated with matrix operations in chord iteration (miter /= 0).

input/output flag, with values and meanings as follows:

vector containing predicted values on entry.

the nordsieck array, an ldyh by lmax array.

a constant >= n, the first dimension of yh.

an error weight vector of length n.

array containing f evaluated at predicted y.

real work space for matrices. in the output, it contains the inverse diagonal matrix if miter = 3 and the lu decomposition of p if miter is 1, 2 , 4, or 5. storage of matrix elements starts at wm(3). storage of the saved jacobian starts at wm(locjs). wm also contains the following matrix-related data: wm(1) = sqrt(uround), used in numerical jacobian step. wm(2) = h*rl1, saved for later use if miter = 3.

integer work space containing pivot information, starting at iwm(31), if miter is 1, 2, 4, or 5. iwm also contains band parameters ml = iwm(1) and mu = iwm(2) if miter is 4 or 5.

output error flag, = 0 if no trouble, 1 if the p matrix is found to be singular.

real work space containing the inverse diagonal matrix if miter = 3 and the lu decomposition of the matrix otherwise. storage of matrix elements starts at wm(3). wm also contains the following matrix-related data: wm(1) = sqrt(uround) (not used here), wm(2) = hrl1, the previous value of h*rl1, used if miter = 3.

integer work space containing pivot information, starting at iwm(31), if miter is 1, 2, 4, or 5. iwm also contains band parameters ml = iwm(1) and mu = iwm(2) if miter is 4 or 5.

the right-hand side vector on input, and the solution vector on output, of length n.

output flag. iersl = 0 if no trouble occurred. iersl = 1 if a singular matrix arose with miter = 3.

flag indicating to save or restore the data:

the message (character array).

the length of msg (number of characters).

the error number (not used).

the error level:

number of integers (0, 1, or 2) to be printed with message.

integer to be printed, depending on ni.

integer to be printed, depending on ni.

number of reals (0, 1, or 2) to be printed with message.

real to be printed, depending on nr.

real to be printed, depending on nr.