07-Jan-2022 18:12:05

collocation_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2.
  Test collocation().

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 =

  Columns 1 through 6

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

  Column 7

         729
       -1458
        2464
          79
           0
           7
         160


y1 =

   1.0e-03 *

    0.1875
    0.9674
         0
         0
         0
         0
         0


  Created plot file "test04.png".

collocation_test():
  Normal end of execution.

07-Jan-2022 18:12:10