Exercises

1. Using Euler's method and a time step of h=1, compute the first ten values of the solution of this ODE:

   

   Step	 tk     tk+1     yk        F(tk,yk)  yk+1
   
      1     0      1.0     1.0       3.0       4.0
   
      2     1.0    2.0     4.0       6.0      10.0
   
      3     2.0    3.0    10.0000    9.4868   19.4868
   
      4     3.0    4.0    19.4868   13.2432   32.7300
   
      5     4.0    5.0    32.7300   17.1630   49.8930
   
      6     5.0    6.0    49.8930   21.1905   71.0835
   
      7     6.0    7.0    71.0835   25.2933   96.3769
   
      8     7.0    8.0    96.3769   29.4515  125.8284
   
      9     8.0    9.0   125.8284   33.6520  159.4804
   
     10     9.0   10.0   159.4804   37.8857  197.3660
   
   

2. Using Euler's method and a time step of h=0.1, compute the first three values of the solution of the ODE:

   

   Step	 tk     tk+1     yk        F(tk,yk)  yk+1
   
      1     0      0.1     1.0000    3.0000    1.3000
   
      2     0.1    0.2     1.3000    3.4205    1.6421
   
      3     0.2    0.3     1.6421    3.8443    2.0265
   
      4     0.3    0.4     2.0265    4.2706    2.4535
   
      5     0.4    0.5     2.4535    4.6991    2.9235
       
      6     0.5    0.6     2.9235    5.1294    3.4364
   
      7     0.6    0.7     3.4364    5.5613    3.9925
   
      8     0.7    0.8     3.9925    5.9944    4.5920
   
      9     0.8    0.9     4.5920    6.4287    5.2348
   
     10     0.9    1.0     5.2348    6.8639    5.9212
   
     11     1.0    1.1     5.9212    7.3001    6.6512    
   

3. Using Euler's method and a time step of h=10^-2, compute the first three values of the solution of this ODE:

   

   Step	 tk     tk+1     yk        F(tk,yk)  yk+1
   
      1     0      0.01    1         3         1.03
      2     0.01   0.02    1.03      3.044667  1.060446
      3     0.02   0.03    1.060446  3.089339  1.091340