Re: Boundary Value Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg7129] Re: Boundary Value Problem
- From: NEWSMGR at selu.edu
- Date: Sun, 11 May 1997 02:57:26 -0400 (EDT)
- Organization: Southeastern Louisiana University
- Sender: owner-wri-mathgroup at wolfram.com
Relay-Version: ANU News - V6.1B9 05/16/94 VAX/VMS V6.2-1H3; site alpha.selu.edu Subject: [mg7129] Re: Boundary Value Problem From: Paul Abbott <paul at physics.uwa.edu.au> To: mathgroup at smc.vnet.net Organization: University of Western Australia On 24 Apr 1997 05:04:15 -0400, "Rick A. Sprague" <sprague at egr.msu.edu> wrote: > > I have > > come to a problem, though, that seems to have stumped MMA. Can the > > following problem be solved with out writing a lengthy MMA program? > > > > y'''''[x]+y[x]==0 > > > > Conditions > > y[0]==0 > > y'[0]==7 > > > > y[1]==1 > > y'[1]==10 > > y''[1]=5 Mathematica can solve this problem directly and exactly -- but the exact solution is quite long and complicated. Here is a simple way of solving the system quasi-numerically: In[1]:= Y = DSolve[y'''''[x] + y[x] == 0, y, x]//First; In[2]:= N[y[0] == 0 /. Y]; In[3]:= N[y'[0] == 7 /. Y]; In[4]:= N[y[1] == 1 /. Y]; In[5]:= N[y'[1] == 10 /. Y]; In[6]:= N[y''[1] == 5 /. Y]; In[7]:= y[x] /. Y /. Chop[First[Solve[{%, %%, %%%, %%%%, %%%%%}, Array[C, 5]]]] Out[7]= 1/5 -191.276 (-1) x -------- + (57.8964 + 9.82354 I) E + x E 3/5 37.7414 - 127.795 I (-1) x ------------------- + (37.7414 + 127.795 I) E + 2/5 (-1) x E 57.8964 - 9.82354 I ------------------- 4/5 (-1) x E Cheers, Paul _________________________________________________________________ Paul Abbott Department of Physics Phone: +61-9-380-2734 The University of Western Australia Fax: +61-9-380-1014 Nedlands WA 6907 paul at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/Paul God IS a weakly left-handed dice player _________________________________________________________________