Consider the following second order differential equation
d2y/dx2 + ady/dx + by = c
With the initial conditions
y(1) = k1, (dy/dx)x=1 = k2
Reduce the second order differential equation to a system of first order differential equations and solve the equations using the FOURTH ORDER Runge-Kutta method for simultaneous equations, to evaluate y(1.2) taking h=0.2 and 0.1, using the following marked data:
| a = |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
110 |
120 |
125 |
| b= |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
| c = |
3 |
9 |
11 |
13 |
15 |
20 |
25 |
30 |
40 |
|
| k1= |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
18 |
20 |
|
| k2= |
1.5 |
-1,5 |
2.5 |
-2.5 |
3.5 |
3.5 |
4.5 |
4.5 |
|
|
• Use MATHEMATICA to improve accuracy of your results taking h=0.05, 0.025 and 0.0125. Attach your Mathematica sheet with your worked solution sheets.
• Specify the accuracy of your calculations in significant figures. All steps in your calculations must be shown in complete detail.