In the Visual Basic Editor by 3QU3z74

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									                               Numerical Solutions of Differential Equations - J. Mahaffy, San Diego State University
                               Want to solve y' = f(x,y) with y(t0) = y0
                    Euler's Method                                            See Sheet 2 for the Runge-Kutta Method
            x0 =             0        y0 =           2          h=        0.1
n        x(n)          y(n)    f(x(n),y(n)) y(n+1)=y(n) + h*f(x(n),y(n))      First step is to adjust the x0, y0, and h values i
     0          0            2 #NAME? #NAME?
     1        0.1    #NAME? #NAME? #NAME?                                     Column B gives the value of the x variable sep
     2        0.2    #NAME? #NAME? #NAME?
     3        0.3    #NAME? #NAME? #NAME?                                     Column C gives the value of the y variable com
     4        0.4    #NAME? #NAME? #NAME?                                      This value comes from the computation in Co
     5        0.5    #NAME? #NAME? #NAME?
     6        0.6    #NAME? #NAME? #NAME?                                     Column D gives the function evaluation using C
     7        0.7    #NAME? #NAME? #NAME?                                       This is the key step in Euler's method. You c
     8        0.8    #NAME? #NAME? #NAME?                                       Next you can go to the Tools on the Menu B
     9        0.9    #NAME? #NAME? #NAME?                                       Visual Basic Editor (or you can take the shor
    10          1    #NAME? #NAME? #NAME?                                       In the Visual Basic Editor, you find the "Publi
    11        1.1    #NAME? #NAME? #NAME?                                       match your particular problem.
    12        1.2    #NAME? #NAME? #NAME?                                       Return to the Excel spreadsheet and go to th
    13        1.3    #NAME? #NAME? #NAME?                                       Enter OK, and the spreadsheet will change t
    14        1.4    #NAME? #NAME? #NAME?                                       Euler's Method. (This also updates Sheet 2 f
    15        1.5    #NAME? #NAME? #NAME?
    16        1.6    #NAME? #NAME? #NAME?
    17        1.7    #NAME? #NAME? #NAME?
    18        1.8    #NAME? #NAME? #NAME?
    19        1.9    #NAME? #NAME? #NAME?
    20          2    #NAME? #NAME? #NAME?
fy, San Diego State University

 t 2 for the Runge-Kutta Method

 is to adjust the x0, y0, and h values in C4, E4, and G4. These change the initial conditions and the stepsize for the problem.

 gives the value of the x variable separated by stepsize h in F4

 gives the value of the y variable computed from Euler's method.
ue comes from the computation in Column E with Euler's formula.

   gives the function evaluation using Columns A and B.
 he key step in Euler's method. You click on D6 to highlight that cell.
 u can go to the Tools on the Menu Bar, then Macros, then select the
Basic Editor (or you can take the shortcut by entering Alt-F11).
 isual Basic Editor, you find the "Public Function f(x,y)" and edit it to
 our particular problem.
  o the Excel spreadsheet and go to the Insert Menu and select Function.
 K, and the spreadsheet will change to the solution in Column C of
Method. (This also updates Sheet 2 for the Runge-Kutta method.)
size for the problem.
                              Want to solve y' = f(x,y) with y(x0) = y0
                    Runge-Kutta Method
            x0 =            0       y0 =           2          h=         0.1
n        x(n)          y(n)      k1          k2          k3           k4       y(n+1) = y(n)+(h/6)*(k1 + 2*k2 + 2*k3 + k4)
     0          0           2 #NAME? #NAME? #NAME? #NAME?                       #NAME?
     1        0.1    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     2        0.2    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     3        0.3    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     4        0.4    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     5        0.5    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     6        0.6    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     7        0.7    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     8        0.8    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
     9        0.9    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    10          1    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    11        1.1    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    12        1.2    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    13        1.3    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    14        1.4    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    15        1.5    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    16        1.6    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    17        1.7    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    18        1.8    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    19        1.9    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
    20          2    #NAME? #NAME? #NAME? #NAME? #NAME?                         #NAME?
(n)+(h/6)*(k1 + 2*k2 + 2*k3 + k4)

								
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