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/* -*- Mode: macsyma; Package: CL-MAXIMA -*- */
/* A collection of all the best ODE routines, run in the*/
/* best (hopefully) order */
/*************************************************/
/* This intitializes the environment when the package gets loaded
or batched */
define_variable(allmethods2,
'[ode2,whittaker,solvehyper,solfac,diffsol,desol,series],
list)$
define_variable(allmethods1,
'[ode2,diffsol,nonlin,nonlin1,riccati],
list)$
define_variable(odetutor,false,boolean)$
define_variable(method,'method,any)$
define_variable(method2,'method2,any)$
define_variable(sings,'sings,any)$
define_variable(ode_routinelist,[],list)$
eval_when([batch,loadfile,translate],block(
/* for DOE MACSYMA, the autoload properties are in max$disk:[ode]ode.lsp */
if not status(feature,nil) or status(feature,cl) then (
ode_routinelist:'[[[abel,lisp,dsk,ode],nonlin,nonlin1],
[[ricsol,lisp,dsk,ode],ricsol],
[[diffac,lisp,dsk,ode],solfac],
[[lapl,lisp,dsk,ode],diffsol],
[[trans,lisp,dsk,ode],desol, deptran,indtran,
invariant,normalform,schwartzian,bothvartran,dadjoint],
[[ricati,lisp,dsk,ode],apollo,riccati],
[[hyper,lisp,dsk,ode],solvehyper],
[[manyt,lisp,dsk,ode],manrecur],
[[series,lisp,dsk,ode],series],
[[whit,lisp,dsk,ode],whittaker],
[[schmid,lisp,dsk,ode],schmidt],
[[intfac,lisp,dsk,ode],int_factor],
[[sings,lisp,dsk,ode],getsings],
[[tran,lisp,dsk,ode],transform],
[[hyp,fasl,dsk,ode],hgfred],
[[remote,lisp,dsk,ell],run_remote],
[[kamke,lisp,dsk,ode],kamke]],
for i in ode_routinelist do apply('setup_autoload,i)),
sstatus(feature,"ode")))$
eval_when([batch,loadfile,translate],block([],
/* for DOE MACSYMA, the autoload properties are in max$disk:[ode]ode.lsp */
if status(feature,cl) then (
ode_routinelist:'[["maxima-source:maxima;abel",nonlin,nonlin1],
["maxima-source:maxima;ricsol",ricsol],
["maxima-source:maxima;diffac",solfac],
["maxima-source:maxima;lapl",diffsol],
["maxima-source:maxima;trans",desol, deptran,indtran,
invariant,normalform,schwartzian,bothvartran,dadjoint],
["maxima-source:maxima;ricati",apollo,riccati],
["maxima-source:maxima;hyper",solvehyper],
["maxima-source:maxima;manyt",manrecur],
["maxima-source:maxima;series",series],
["maxima-source:maxima;whit",whittaker],
["maxima-source:maxima;schmid",schmidt],
["maxima-source:maxima;intfac",int_factor],
["maxima-source:maxima;sings",getsings],
["maxima-source:maxima;tran",transform],
["maxima-source:maxima;hyp",hgfred],
["maxima-source:maxima;remote",run_remote],
["maxima-source:maxima;kamke",kamke]],
for i in ode_routinelist do apply('setup_autoload,i)),
sstatus(feature,"ode")))$
/* This intitializes the environment for TRANSLATION,
loads modedeclarations, for the whole package, macro packages, etc. */
/* EVAL_WHEN([TRANSLATE],?PRINC('?"
WE ARE TRANSLATING AWAY!
",?TYO))$ */
odeaux(eq,oldy,oldx,option):=block([dd,ans,solutionlist,x,y],
eq:subsf(eq,oldy,oldx),
return(subst(oldy,y,subst(oldx,x,solveode(eq,y,x,option)))))$
solveode(eq,y,x,option):=block([dd,ans,solutionlist],
eq:eqsimp(eq),
dd:derivdegree(eq,y,x),
if option=[] or option=['any] then (
if(dd=1) then (
if(ans:win('ode2,eq,y,x))#false then return(ans),
if(testli(rhs(eq)-lhs(eq),y,x))=true then
(if(ans:win('diffsol,eq,y,x))#false then
(method:"LAPLACE XFORM", return(ans))) else
(if(ans:win('nonlin,eq,y,x))#false then
(method:"NONLIN IN YPRIME", return (ans)),
if(ans:win('nonlin1,eq,y,x))#false then
(method:"NONLIN XFORM", return (ans)),
if riccati_test(lhs(eq)-rhs(eq),y,x)=true then
if(ans:win('riccati,eq,y,x))#false then
(method:"RICCATI",return(ans)),
if(ans:win('int_factor,eq,y,x))#false then
(method:"FOUND EULER MULTIPLIER",return(ans))
)) else
( /*These methods are tailored for order = 2 */
if dd=2 then(
if(ans:win('ode2,eq,y,x))#false then return(ans),
if(ans:win('desol,eq,y,x))#false then (method:'method1,return(ans)),
if(ans:win('diffsol,eq,y,x))#false then
(method:"LAPLACE XFORM",return(ans)),
if(length(sings:getsings(eq,y,x))=3) then
if(ans:win('solvehyper,eq,y,x))#false then(method:'HYPERGEOMETRIC,
return(ans)),
if(sings='[0,inf] ) then
if(ans:win('whittaker,eq,y,x))#false then(method:"CONFLUENT HYPER",
return(ans)),
if(ans:win('solfac,eq,y,x))#false then
(method:"FACTOR OPERATOR",return(ans)),
if(ans:win('series,eq,y,x))#false then (method:"SERIES",
return(ans))) else
if (ans:win('diffsol,eq,y,x))#false then (method:"LAPLACE XFORM",
return(ans)),
method:"NONE",return(false)))
else(
if option=['all] then
if dd=2 then option:allmethods2 else if dd=1 then option:allmethods1
else option:['diffsol],
solutionlist:map(lambda([u],win(u,eq,y,x)),option),
if (length(solutionlist)=1) then
if programmode#true then
solutionlist:part(solutionlist,1),
return(solutionlist)))$
win(fun,eq,y,x):= block([ans],
if odetutor=true then print( "TRYING ",fun),
if((ans:errcatch(block(method2:fun,apply(method2,[eq,y,x])))=[]))then 'fun,
/* commented out of DOE MACSYMA since the GC statistics are on by default
if ?cadr(status(freecore))=0 then error("out of core...sorry"), */
if (ans=[false] or ans=[]) then return(false)
else return(part(ans,1)))$
homog(eq,y,x):=block([eq1,p1,q1,hom,h1],
eq1:lhs(eq)-rhs(eq),
p1:p(eq1,y,x),q1:q(eq1,y,x),
hom:diff(y,x,2)+p1*diff(y,x)+q1*y,
if((h1:radcan(eq1-hom))=0) then return(false) else
return(hom=-h1))$
purify(sol,y,x):=block([sol1,s1,s2,%k1,%k2],
sol1:rhs(sol),
s1:ratcoef(sol1,%k1),s2:ratcoef(sol1,%k2),
if(s1=0) then if(s2=0) then return(false) else s1:s2,
if(length(s1)>length(s2)) then s1:s2,
return(s1))$
testli(de,y,x):=block([h],
de:expand(de),
h:hipow(de,diff(y,x)),
if(h#1)then return(false),h:[],
h:cons(ratcoef(de,diff(y,x)),h),
h:cons(ratcoef(de,y,1),h),
h:cons(ratcoef(de,y,0),h),
if(hipow(de,y)#1) then return(false),
h:cons(ratcoef(de,diff(y,x,2)),h),
if not freeof(y,h) then return(false) else
return(true))$
/*Simplifies an ODE removes factors common to all terms*/
eqsimp(de):=block([inflag:true],
de:factor(lhs(de)-rhs(de)),
if(atom(de) or not(inpart(de,0)="*")) then return(de=0),
de:map(lambda([v],if freeof(nounify('diff),v) then 1 else v),de),
return(de=0))$
subsf(eq,oldy,oldx):=block([%%newy,y,x],
depends(y,x),
eq:subst(%%newy,oldy,eq),
eq:subst(x,oldx,eq),
eq:subst(y,%%newy,eq),
return(eq))$
riccati_test(de,y,x):=block([q],de:expand(de),
if hipow(de,'diff(y,x))#1 then return(false),
if ((q:lopow(de,'diff(y,x)))#1 and q#0) then return(false),
if hipow(de,y)=2 then return(true) else return(false))$
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