RSP examples of the AnalyticalApproximations`LdeApprox` package
Copyright © 2003-20011DigiArea, Inc.. All rights reserved.
This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of doing polynomial approximation of a solution of an LDE with regular singular points.
This loads the package.
In[119]:=
Example 1
Simple boundary value problem.
In[120]:=
Finding polynomial approximation for solution of the BVP.
In[121]:=
Out[121]=
Using Mathematica function DSolve to get exact solution of the BVP.
In[122]:=
Out[122]=
More compact result is as follows.
In[123]:=
Out[123]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[124]:=
Out[124]=
Comparing exact and approximate results for n = 3.
In[125]:=
Out[125]=
Example 2
Boundary value problem.
In[126]:=
Out[126]=
Finding polynomial approximation for solution of the BVP.
In[127]:=
Out[127]=
Using Mathematica function DSolve to get exact solution of the BVP.
In[128]:=
Out[128]=
In fact the result is as follows.
In[129]:=
Out[129]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[130]:=
Out[130]=
Example 3
Boundary value problem.
In[131]:=
Out[131]=
Finding polynomial approximation for solution of the BVP.
In[132]:=
Out[132]=
Using Mathematica function DSolve to get exact solution of the BVP.
In[133]:=
Out[133]=
More compact result is as follows.
In[134]:=
Out[134]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[135]:=
Out[135]=
Example 4
Boundary value problem.
In[136]:=
Out[136]=
Finding polynomial approximation for solution of the BVP.
In[137]:=
Out[137]=
Unfortunately DSolve can not find exact solution of the BVP.
In[138]:=
Out[138]=
Nevertheless the exact solution is as follows.
In[139]:=
Out[139]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[140]:=
Out[140]=
Example 5
Boundary value problem.
In[141]:=
Out[141]=
Finding polynomial approximation for solution of the BVP.
In[142]:=
Out[142]=
Exact solution of the BVP.
In[143]:=
Out[143]=
More compact result.
In[144]:=
Out[144]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[145]:=
Out[145]=
Example 6
Boundary value problem.
In[146]:=
Out[146]=
Finding polynomial approximation for solution of the BVP.
In[147]:=
Out[147]=
Unfortunately DSolve can not find exact solution of the BVP.
In[148]:=
Out[148]=
Nevertheless the exact solution is as follows.
In[149]:=
Out[149]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[150]:=
Out[150]=
Example 7
Boundary value problem.
In[151]:=
Out[151]=
Finding polynomial approximation for solution of the BVP.
In[152]:=
Out[152]=
Unfortunately DSolve can not find exact solution of the BVP.
In[153]:=
Out[153]=
Nevertheless the exact solution is as follows.
In[154]:=
Out[154]=
Comparing exact and approximate results using Mathematica function Plot3D.
In[155]:=
Out[155]=
