Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... a differential equation: dQ=dh = q(h) Q(a) Q a : 3) Practical codes often include additional safety factors and restrictions on changes in h on heuristic grounds [12] for a suitable choice of (a; Q a ) here (0; 0) Finding h : Q(h here thus reduces to a standard g stop problem [4]. However, switching co ordinates and noting that h is monotonic in Q for Q 0, solving dh=dQ = 1=q(h(Q) h(Q a ) a; 4) we can in principle find a suitable EPS stepsize estimator h directly, by integrating (4) across [Q a ; Numerically, however, due to the initial singularity, a; Q a ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

....codes typically ignore such cases. An example of this occurs in DELSOL [10, 13] Where full lag function derivative information is available, however, one possible approach to this problem makes use of Roll e s theorem [5] Such techniques have also been proposed for ODE g stop methods in [1]. Providing ff(t) is continuous, if a second root ff( j exists, ff (j) must vanish for some j 2 [t n ; t n 1 ] It follows that if ff (t) is root free on [t n ; t n h] ff(t) cannot recross j . Information about ff (t) could hence be used to help stepsize selection and so ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

.... respect to h we note, however, that 1 (h) q(s) ds and 00 1 (h) q(h) Given this, Q 1 may be redefined in terms of a differential equation = Q 2 (8) q(h) for h 0 given Q = 0 where Q = Q 1 ; Q 2 ] Solving for h such that then reduces to a so called g stop problem [3]. Reversing coordinates (9) and noting that h is monotone in Q 1 for Q 1 0, we observe however that given suitable starting values for (a; Q(a) integrating (9) across [Q 1 (a) provides a simple direct expression for the required stepsize h = h( This is our key advance. Given a ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

.... equation: dQ=dh = q(h) Q(a) Q a : 3) 2 Practical codes often include additional safety factors and restrictions on changes in h on heuristic grounds [12] 3 for a suitable choice of (a; Q a ) here (0; 0) Finding h : Q(h ) here thus reduces to a standard g stop problem [4]. However, switching co ordinates and noting that h is monotonic in Q for Q 0, solving dh=dQ = 1=q(h(Q) h(Q a ) a; 4) we can in principle find a suitable EPS stepsize estimator h directly, by integrating (4) across [Q a ; Numerically, however, due to the initial singularity, a; Q a ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

....0 1 (h) Z h 0 q(s) ds and Q 00 1 (h) q(h) Given this, Q 1 may be redefined in terms of a differential equation dQ 1 dh = Q 2 (8) dQ 2 dh = q(h) for h 0 given Q = 0 where Q = Q 1 ; Q 2 ] T . Solving for h such that Q 1 (h ) then reduces to a so called g stop problem [3]. Reversing coordinates dh dQ 1 = 1 Q 2 (h) 9) dQ 2 dQ 1 = q(h) Q 2 (h) and noting that h is monotone in Q 1 for Q 1 0, we observe however that given suitable starting values for (a; Q(a) integrating (9) across [Q 1 (a) provides a simple direct expression for the required ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

....codes typically ignore such cases. An example of this occurs in DELSOL [10, 13] Where full lag function derivative information is available, however, one possible approach to this problem makes use of Roll e s theorem [5] Such techniques have also been proposed for ODE g stop methods in [1]. Providing ff(t) is continuous, if a second root ff( j exists, ff 0 (j) must vanish for some j 2 [t n ; t n 1 ] It follows that if ff 0 (t) is root free on [t n ; t n h] ff(t) cannot recross 0 j . Information about ff 0 (t) could hence be used to help stepsize selection ....

Corliss, G. and Chang, Y. F. "Multiple g-stop facility in ATOMFT -- a Taylor series ODE solver." An address given at the 1988 conference on the numerical solution of initial value problems for ordinary differential equations, Toronto, Ontario, Canada.

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