solving DE numerically....
- To: mathgroup at smc.vnet.net
- Subject: [mg126690] solving DE numerically....
- From: raj kumar <rajesh7796gm at gmail.com>
- Date: Thu, 31 May 2012 02:48:36 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
hi all,
greetings from sunny malaysia!
this pertains to solving a DE numerically at 5 differnt points.Should be straigth forward. But i get different results when i try to insert one parameter "by hand".have i overlooked something?
any feed-back will be most appreciated
Please consider the following:
In[137]:= pw3 = Piecewise[{{V0, x < a}, {V0, x == a}}, 0];
k = Sqrt[10 - pw3];
V0 = -1;
a = 2;
Table[{x, k}, {x, 1, 5}]
(*Plot[Piecewise[{{V0, x<a}, {V0,x==a}},0],{x,0,5}]*)
Out[141]= {{1, Sqrt[11]}, {2, Sqrt[11]}, {3, Sqrt[10]}, {4, Sqrt[
10]}, {5, Sqrt[10]}}
Solve the following DE numerically for y1[
1.0], y1[2.0], y1[3], y1[4], y1[5]
In[148]:=
s33 = NDSolve[{(y1^\[Prime]\[Prime])[x] + Sqrt[k] y1[x] == 0,
y1[0.1] == 0, Derivative[1][y1][0.1] == 1/10^6}, y1, {x, 1, 10}];
We obtain
In[149]:= {y1[1.0], y1[2.0], y1[3], y1[4], y1[5]} /. s33
Out[149]= {{6.9408*10^-7,
4.08303*10^-7, -5.09458*10^-7, -6.64851*10^-7, 1.70684*10^-7}}
now check the output above for the values x =
1 to x = 5. For x = 1, 2,
we insert k =
Sqrt[11] by hand in the same DE above and work out the values for \
the same points again. We get
In[144]:=
s11 = NDSolve[{(y11^\[Prime]\[Prime])[x] + Sqrt[ 11] y11[x] == 0,
y11[0.1] == 0, Derivative[1][y11][0.1] == 1/10^6},
y11, {x, 1, 10}];
In[145]:= {y11[1.0], y11[2.0]} /. s11
Out[145]= {{5.47931*10^-7, -1.68202*10^-7}}
Out[105]= {{5.47931*10^-7, -1.68202*10^-7}}
For x = 3, 4, 5, k = Sqrt[10]. We get
In[146]:=
s11 := NDSolve[{(y11^\[Prime]\[Prime])[x] + Sqrt[10] y11[x] == 0,
y11[0.1] == 0, Derivative[1][y11][0.1] == 1/10^6},
y11, {x, 1, 10}];
In[147]:= {y11[3], y11[4], y11[5]} /. s11
Out[147]= {{-5.30318*10^-7, 3.34051*10^-7, 4.16315*10^-7}}
Qn : Should the values for y11[1-5] be any different from that calculated earlier ie y1[1-5]?