The following data gives the velocity of a particle for 8 seconds at an interval of 2 seconds. Find the initial acceleration using all the data.
Time (sec)
Velocity
0
0
2
172
4
1304
6
4356
8
10288
( m /sec)
2. Find f (2.5), f' (2) and f ^ prime prime 2.5) using Newton's backward difference method.
f(x)
1.0
3.7183
15
5.4817
2.0
8.3891
25
13.1825
3. Solve by factorization/triangularization method the following system of equations:
3x_{1} + x_{2} - 3x_{3} = - 4 x_{1} + x_{2} + 2x_{3} = 4 2x_{1} - 3x_{2} - 5x_{3} = - 5
4. Solve the system of equations by the Gauss-Seidal iteration method. Take the initial approximation as x ^ (1) = 0 y ^ (1) = 0 and z ^ (1) = 0 .
3x + 8y + 29z = 71 7x + 52y + 13x = 104 83x + 11y - 4z = 95
5. Solve the equation d/dx (y) = - 2x * y ^ 2 with initial condition y(0) = 1 by the Runge-Kutta method of order 4 for x = 0.2 and 0.4 with h = 0.2
