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/* ode1_nonlinear.mac
Driver routine for first order nonlinear ODE routines
Copyright (C) 2004 David Billinghurst
This program 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.
This program is distributed in the 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 this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
put('ode1_nonlinear,001,'version)$
if get('ode1_clairault,'version)=false then
load("ode1_clairault.mac")$
if get('ode1_lagrange,'version)=false then
load("ode1_lagrange.mac")$
if get('ode1_riccati,'version)=false then
load("ode1_riccati.mac")$
if get('ode1_lie,'version)=false then
load("ode1_lie.mac")$
if get('ode1_factor,'version)=false then
load("ode1_factor.mac")$
if get('ode1_abel,'version)=false then
load("ode1_abel.mac")$
ode1_nonlinear(de,y,x):=block(
[q,q2],
ode_disp(" in ode1_nonlinear"),
ode_disp(" -> ode1_factor"),
q:ode1_factor(de,y,x),
if (is(q#false)) then return(q),
ode_disp(" -> ode1_clairault"),
q:ode1_clairault(de,y,x),
if (is(q#false)) then return(q),
ode_disp(" -> ode1_lagrange"),
q:ode1_lagrange(de,y,x),
if (is(q#false)) then return(q),
/* Sometimes ode1_lie() can solve Riccati equations
that are only partially solved by ode1_riccati() */
ode_disp(" -> ode1_riccati"),
q:ode1_riccati(de,y,x),
if (is(q#false)) then return( block(
if not(freeof(%u,q)) then (
q2:ode1_lie_wrapper(de,y,x),
if (is(q2#false)) then q:q2
),
[q])
),
ode_disp(" -> ode1_abel"),
q:ode1_abel(de,y,x),
/* Give up if return [] */
if (q=[]) then return(false),
if (is(q#false)) then return(q),
ode_disp(" -> ode1_lie"),
q:ode1_lie_wrapper(de,y,x),
if (is(q#false)) then return([q]),
return(false)
)$
/* Wrapper for ode1_lie() */
ode1_lie_wrapper(de,y,x) := block(
[phi],
phi:solve(lhs(de)-rhs(de),'diff(y,x)),
if (is(phi=[])) then
false
else
phi:rhs(first(phi)),
ode1_lie(phi,y,x)
)$
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