20-Dec-2018 15:59:59

COLLOCATION_TEST
  MATLAB version.
  Test the COLLOCATION library.

COLLOCATION_TEST01:
  Collocate the equation F(X)=SIN(X)
  Let N be the number of collocation points.
  Choose N points X in [0,2Pi].
  Let G(X) be a polynomial of degree N-1.
    G(X(1:N)) = SIN(X(1:N))
  is N equations for the N unknown coefficients in G.

  Created plot file "test01.png".

COLLOCATION_TEST02:
  Collocate a two point boundary value problem.
  Let N be the number of collocation points.
  Choose N points X in [0,2].
  Let G(X) be a polynomial of degree N-1.
    G(X(1)=0.0) = 1.0
    G"(X(2:N-1)) = G(X(2:N-1))
    G(X(N)=2.0) = exp(2.0)
  is N equations for the N unknown coefficients in G.

  Created plot file "test02.png".

COLLOCATION_TEST03:
  Collocate a two point boundary value problem.
  Let N be the number of collocation points.
  Choose N points X in [0,2].
  Let G(X) be C1+C2*X+C(3:N)*SIN((1:N-2)*PI*X/(N-2)).
    G(X(1)=0.0) = 1.0
    G"(X(2:N-1)) = G(X(2:N-1))
    G(X(N)=2.0) = exp(2.0)
  is N equations for the N unknown coefficients in G.

  Created plot file "test03.png".

COLLOCATION_TEST04:
  Collocate a second order initial value ODE.
  Let N be the number of collocation points.
  Choose N points X in [-3,2].
  Let G(X) be a polynomial in X of degree N.
    G(-3) = A
    G'(-3) = B
    G"(X(I)) - 6 G'(X(I) + 13 G(X(I)) = 0, I = 2...N
  is N equations for the N unknown coefficients in G.
A =

      1     -3      9    -27     81   -243    729
      0      1     -6     27   -108    405  -1458
     13    -32     78   -188    448  -1056   2464
     13    -19     27    -37     49    -63     79
     13     -6      2      0      0      0      0
     13      7      3      1      1      3      7
     13     20     30     44     64     96    160

y1 =

   1.8746e-04
   9.6739e-04
   0.0000e+00
   0.0000e+00
   0.0000e+00
   0.0000e+00
   0.0000e+00


  Created plot file "test04.png".

COLLOCATION_TEST
  Normal end of execution.

20-Dec-2018 16:00:00