ivpNondimensional/ivpNonNew/ivp.a4c

REQUIRE "atoms.a4l";

(*
 *  ivp.a4c
 *  by Arthur W. Westerberg
 *  Part of the ASCEND Library
 *  $Date: 06/16/2006 $
 *  $Revision: 1.0 $
 *
 *  This file is part of the ASCEND Modeling Library.
 *
 *  Copyright (C) 1994 - 2006 Carnegie Mellon University
 *
 *  The ASCEND Modeling Library is free software; you can redistribute
 *  it and/or modify it under the terms of the GNU General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  The ASCEND Modeling Library is distributed in hope that it
 *  will be useful, but WITHOUT ANY WARRANTY; without even the implied
 *  warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *  See the GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with the program; if not, write to the Free Software
 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA.  Check
 *  the file named COPYING.
 *)

(*============================================================================

    I V P  .  A 4 C
    -----------------------------

    AUTHOR:      Arthur W. Westerberg

    DATES:       06/2006 - Original code (AWW)
    
    CONTENTS:	 Models for the numerical integration equations for
                 the two multistep methods: a bdf for stiff problems
		 and the Adams Moulton for non-stiff problems.  There
		 is also a framework within which one creates the
		 model for the physical system.  These models are for
		 taking one step of the independent variable.

============================================================================*)


(* ---------------------------------------------------------- *)

MODEL ivpBase;
END ivpBase;

(* ---------------------------------------------------------- *)

MODEL diff(
    y                WILL_BE factor;
    dydt             WILL_BE factor;
    t                WILL_BE factor;
) REFINES ivpBase;
    
END diff;

(* ---------------------------------------------------------- *)

MODEL diff12Step(
    y                WILL_BE factor;
    dydt             WILL_BE factor;
    t                WILL_BE factor;
) REFINES diff;


    a[0..12]         IS_A factor;
    dt[0..12]        IS_A factor;
    yPast[0..12]     IS_A factor;
    dydtPast[0..12]  IS_A factor;
    tPast[0..12]     IS_A factor;
    
    yPast[0] = y;
    dydtPast[0] = dydt;
    dt[0] = t;
    
    FOR i IN 0..12 CREATE
	dt[i] = tPast[i] - t;
	valueP[i]    IS_A valuePoly(yPast[i], dt[i], a);
	derivP[i]    IS_A derivPoly(dydtPast[i], dt[i], a);
    END FOR;

END diff12Step;

(* ---------------------------------------------------------- *)

MODEL valuePoly12(
    y                WILL_BE factor;
    dt               WILL_BE factor;
    a[0..,12]        WILL_BE factor;
) REFINES ivpBase;
    
    (* y is an algebraic variable for which prediction will be done as
      one marches when solving *)
    
    (* a[i] in the polynomial as written below approximates the i-th
      derivative of y wrt t (as in a Taylors Series expansion) *)

     polyValue: y = a[0]
       + dt*(a[1]
       + dt*(a[2]/2
       + dt*(a[3]/6
       + dt*(a[4]/24
       + dt*(a[5]/120
       + dt*(a[6]/720
       + dt*(a[7]/5040
       + dt*(a[8]/40320
       + dt*(a[9]/362880
       + dt*(a[10]/3628800
       + dt*(a[11]/39916800
       + dt*(a[12]/479001600))))))))))));
       
END valuePoly12;

(* ---------------------------------------------------------- *)

MODEL derivPoly12(
    dydt           WILL_BE factor;
    y              WILL_BE factor;
    dt             WILL_BE factor;
    a[0..12]       WILL_BE factor;
) REFINES ivpBase;

    (* dydt is the derivative of the state variable y with respect to
      the independent variable dt.  dt is the value of t for this
      point less the current value of t (i.e., we are writing the
      polynomial in dt where dt = 0 is the current point). *)
    
    (* a[i] in the polynomial as written below approximates the i-th
      derivative of y wrt t (as in a Taylors Series expansion) *)
    
    polyDeriv: dydt = a[1]
       + dt*(a[2]
       + dt*(a[3]/2
       + dt*(a[4]/6
       + dt*(a[5]/24
       + dt*(a[6]/120
       + dt*(a[7]/720
       + dt*(a[8]/5040
       + dt*(a[9]/40320
       + dt*(a[10]/362880
       + dt*(a[11]/3638800
       + dt*(a[12]/39916800)))))))))));

END derivPoly12;
1	REQUIRE "atoms.a4l";
2
3	(*
4	* ivp.a4c
5	* by Arthur W. Westerberg
6	* Part of the ASCEND Library
7	* $Date: 06/16/2006 $
8	* $Revision: 1.0 $
9	*
10	* This file is part of the ASCEND Modeling Library.
11	*
12	* Copyright (C) 1994 - 2006 Carnegie Mellon University
13	*
14	* The ASCEND Modeling Library is free software; you can redistribute
15	* it and/or modify it under the terms of the GNU General Public
16	* License as published by the Free Software Foundation; either
17	* version 2 of the License, or (at your option) any later version.
18	*
19	* The ASCEND Modeling Library is distributed in hope that it
20	* will be useful, but WITHOUT ANY WARRANTY; without even the implied
21	* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
22	* See the GNU General Public License for more details.
23	*
24	* You should have received a copy of the GNU General Public License
25	* along with the program; if not, write to the Free Software
26	* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check
27	* the file named COPYING.
28	*)
29
30	(*============================================================================
31
32	I V P . A 4 C
33	-----------------------------
34
35	AUTHOR: Arthur W. Westerberg
36
37	DATES: 06/2006 - Original code (AWW)
38
39	CONTENTS: Models for the numerical integration equations for
40	the two multistep methods: a bdf for stiff problems
41	and the Adams Moulton for non-stiff problems. There
42	is also a framework within which one creates the
43	model for the physical system. These models are for
44	taking one step of the independent variable.
45
46	============================================================================*)
47
48
49	(* ---------------------------------------------------------- *)
50
51	MODEL ivpBase;
52	END ivpBase;
53
54	(* ---------------------------------------------------------- *)
55
56	MODEL diff(
57	y WILL_BE factor;
58	dydt WILL_BE factor;
59	t WILL_BE factor;
60	) REFINES ivpBase;
61
62	END diff;
63
64	(* ---------------------------------------------------------- *)
65
66	MODEL diff12Step(
67	y WILL_BE factor;
68	dydt WILL_BE factor;
69	t WILL_BE factor;
70	) REFINES diff;
71
72
73	a[0..12] IS_A factor;
74	dt[0..12] IS_A factor;
75	yPast[0..12] IS_A factor;
76	dydtPast[0..12] IS_A factor;
77	tPast[0..12] IS_A factor;
78
79	yPast[0] = y;
80	dydtPast[0] = dydt;
81	dt[0] = t;
82
83	FOR i IN 0..12 CREATE
84	dt[i] = tPast[i] - t;
85	valueP[i] IS_A valuePoly(yPast[i], dt[i], a);
86	derivP[i] IS_A derivPoly(dydtPast[i], dt[i], a);
87	END FOR;
88
89	END diff12Step;
90
91	(* ---------------------------------------------------------- *)
92
93	MODEL valuePoly12(
94	y WILL_BE factor;
95	dt WILL_BE factor;
96	a[0..,12] WILL_BE factor;
97	) REFINES ivpBase;
98
99	(* y is an algebraic variable for which prediction will be done as
100	one marches when solving *)
101
102	(* a[i] in the polynomial as written below approximates the i-th
103	derivative of y wrt t (as in a Taylors Series expansion) *)
104
105	polyValue: y = a[0]
106	+ dt*(a[1]
107	+ dt*(a[2]/2
108	+ dt*(a[3]/6
109	+ dt*(a[4]/24
110	+ dt*(a[5]/120
111	+ dt*(a[6]/720
112	+ dt*(a[7]/5040
113	+ dt*(a[8]/40320
114	+ dt*(a[9]/362880
115	+ dt*(a[10]/3628800
116	+ dt*(a[11]/39916800
117	+ dt*(a[12]/479001600))))))))))));
118
119	END valuePoly12;
120
121	(* ---------------------------------------------------------- *)
122
123	MODEL derivPoly12(
124	dydt WILL_BE factor;
125	y WILL_BE factor;
126	dt WILL_BE factor;
127	a[0..12] WILL_BE factor;
128	) REFINES ivpBase;
129
130	(* dydt is the derivative of the state variable y with respect to
131	the independent variable dt. dt is the value of t for this
132	point less the current value of t (i.e., we are writing the
133	polynomial in dt where dt = 0 is the current point). *)
134
135	(* a[i] in the polynomial as written below approximates the i-th
136	derivative of y wrt t (as in a Taylors Series expansion) *)
137
138	polyDeriv: dydt = a[1]
139	+ dt*(a[2]
140	+ dt*(a[3]/2
141	+ dt*(a[4]/6
142	+ dt*(a[5]/24
143	+ dt*(a[6]/120
144	+ dt*(a[7]/720
145	+ dt*(a[8]/5040
146	+ dt*(a[9]/40320
147	+ dt*(a[10]/362880
148	+ dt*(a[11]/3638800
149	+ dt*(a[12]/39916800)))))))))));
150
151	END derivPoly12;