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NUMERICAL SOLUTION OF ODE'S - 19/08/02) / ENVIRONMENTAL FLUID MECHANICS LAB / DEPT OF CIVIL AND ENVIRONMENTAL ENGINEERİNG / STANFORD UNIVERSITY * * LOTKA–VOLTERRA EQUATION CON(F0,S0,TMAX) CON(ALPHA,BETA,GAMMA,EPS) 1DF = ALPHA*F-BETA*F*S F = INT(1DF,F0) 1DS = EPS*BETA*F*S-GAMMA*S S = INT(1DS,S0) HDR(TIME,FISH,SHARK) OUT(T,F,S) PLO(F,S) FIN(T,TMAX) END <EOR> 600. 50. 50. 0.7 0.007 0.5 0.1 <EOF>
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The MIMIC software package, written as FORTRAN overlay programs, executes input statements of the mathematical model in six consecutive passes. Simulation programs written in MIMIC are compiled rather than interpreted. The core of the simulation package is a variable step numerical integrator of
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Card columns 0 1 2 3 4 5 6 7 12345678901234567890123456789012345678901234567890123456789012345678901 ----------------------------------------------------------------------- * A SIMPLE PREDATOR-PREY MODEL FROM MARINE BIOLOGY / (TUTORIAL 2:
126:. Many useful functions related to electrical circuit elements exist besides some mathematical functions found in most scientific programming languages. There is no need to sort the statements in order of dependencies of the variables, since MIMIC does it internally.
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Control Data MIMIC; A Digital
Simulation Language, Reference Manual, Publication Number 4461n400, Control Data Corporation, Special Systems Publications, St. Paul, Minnesota (April 1968)
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in several scientific disciplines as in engineering, physics, chemistry, biology, economics and as well as in social sciences can easily be solved by
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757:. Stanford University-Dept of Civil and Environmental Engineering, Environmental Fluid Mechanics Lab. 2002-08-19. Archived from
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MIMIC, An
Alternative Programming Language for Industrial Dynamics, N.D. Peterson, Socio-Econ Plan Sci. 6, Pergamon 1972
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and the results of the analysis are listed or drawn in diagrams. It also enables the analysis of
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to determine the dynamics of fish and shark populations. As a simple model, we choose the
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MIMCO (compiler) – compiles the user program and creates an in-core array of instructions,
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This article is about the programming language. For the vaccine development tool, see
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continuous block simulation language, but capable of incorporating blocks of
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41:, F. J. Sansom and L. M. Warshawsky of Systems Engineering Group within the
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MIMSO (sort)– sorts the instructions array after dependencies of variables,
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312:: death rate per encounter of fish with sharks (1/sharks and year).
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334:: death rate of sharks in the absence of their prey, fish (1/year)
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MIMOUT (output)– puts out the data as a list or diagram of data.
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356:: efficiency of turning predated fish into sharks (sharks/fish)
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99:, MIMIC is capable of solving much larger simulation models.
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MIMIC Manual (1969), Computer Center Oregon State
University
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MIMEX (execute)– executes the user program by integrating,
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MIMIN (input)– reads in user simulation program and data,
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design. Written completely in FORTRAN but one routine in
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460:{\displaystyle {\dot {s}}=\epsilon \beta fs-\gamma s}
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172:Consider a predator-prey model from the field of
129:Parts of the software organized in overlays are:
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268:: growth rate of shark population (sharks/year)
30:, known in capitalized form only, is a former
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406:{\displaystyle {\dot {f}}=\alpha f-\beta fs}
232:: growth rate of fish population (fish/year)
64:MIMIC is a further development from MIDAS (
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752:"Tutorial 2: Numerical Solutions of ODE's"
196:(t): Shark population over time (sharks)
180:and the constants given in a tutorial.
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561:The problem's constants are given as:
1128:Programming languages created in 1964
1103:Object-oriented programming languages
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190:(t): Fish population over time (fish)
740:Defense Technical Information Center
13:
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1118:Control Data Corporation software
142:MIMAS (assembler) – converts the
1113:Simulation programming languages
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1123:Wright-Patterson Air Force Base
1108:Numerical programming languages
104:ordinary differential equations
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84:imulator), which represented
116:nonlinear dynamic conditions
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664:= 0.007 fish/shark and year
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551:{\displaystyle s(0)=s_{o}}
508:{\displaystyle f(0)=f_{o}}
261:{\displaystyle {\dot {s}}}
225:{\displaystyle {\dot {f}}}
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53:, United States. It is an
43:Air Force Materiel Command
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1000:Chippewa Operating System
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701:{\displaystyle \epsilon }
349:{\displaystyle \epsilon }
830:Control Data Corporation
470:with initial conditions
1050:PLATO (computer system)
679:{\displaystyle \gamma }
635:{\displaystyle \alpha }
327:{\displaystyle \gamma }
283:{\displaystyle \alpha }
178:Lotka–Volterra equation
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305:{\displaystyle \beta }
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22:Mimic (disambiguation)
20:. For other uses, see
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613:{\displaystyle s_{o}}
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584:{\displaystyle f_{o}}
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148:machine-oriented code
112:numerical integration
1059:Affiliated companies
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55:expression-oriented
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37:developed 1964 by
18:MIMIC (Immunology)
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708:= 0.1 shark/fish
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642:= 0.7 fish/year
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61:-like algebra.
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39:H. E. Petersen
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934:CDC Cyber 200
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764:on 2010-07-20
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1061:and products
987:
929:CDC STAR-100
849:Seymour Cray
766:. Retrieved
759:the original
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102:With MIMIC,
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94:Control Data
81:
77:
73:
69:
65:
63:
51:Dayton, Ohio
27:
26:
1068:ETA Systems
969:Languages:
716:Code sample
620:= 50 sharks
106:describing
72:ntegration
1097:Categories
1005:CDC Kronos
837:Key people
768:2012-02-26
727:References
591:= 600 fish
32:simulation
1082:Cray Inc.
1022:CDC SCOPE
947:CDC Cyber
867:Computers
696:ϵ
674:γ
652:β
630:α
452:γ
449:−
440:β
437:ϵ
428:˙
395:β
392:−
386:α
377:˙
344:ϵ
322:γ
300:β
278:α
253:˙
217:˙
1040:CDC Wren
956:Software
911:CDC 8600
906:CDC 7600
899:CDC 6600
884:CDC 1700
874:CDC 1604
239:/ dt or
203:/ dt or
68:odified
973:COMPASS
166:Problem
161:Example
90:COMPASS
76:igital
59:FORTRAN
45:at the
1015:NOS/VE
921:Vector
80:nalog
1073:ETA10
988:MIMIC
983:Cybil
978:SYMPL
780:Notes
762:(PDF)
755:(PDF)
360:then
28:MIMIC
996:OS:
1010:NOS
963:026
183:If
144:BCD
49:in
1099::
118:.
822:e
815:t
808:v
771:.
606:o
602:s
577:o
573:f
544:o
540:s
536:=
533:)
530:0
527:(
524:s
501:o
497:f
493:=
490:)
487:0
484:(
481:f
455:s
446:s
443:f
434:=
425:s
401:s
398:f
389:f
383:=
374:f
250:s
237:s
235:d
214:f
201:f
199:d
194:s
188:f
150:,
82:S
78:A
74:D
70:I
66:M
24:.
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