PART 8

The voltage v across a capacitor at time t seconds is given by the following table:
9

| ० | 2 | 4 | | 6 | 8 |
150 | 63 | 28 | 12 | 5.6

Use the method of least squares to fit a curve of the form ४ = aekt to this data.

A rocket is launched from the ground. Its acceleration is registered during the 9 first
80 seconds and is given in the table below. Using Simpson's 1/3 rd rule, find the
velocity of the rocket at t = 80 seconds.

t (sec) 0] 10 | 20 | 30 | 40 | 50 | 60 | 70 80

f(cm/sec2) | 30 | 31.63 | 33.34 | 35.47 | 37.75 | 40.33 | 43.25 | 46.69 | 50.67

Using Runge-Kutta method of order 4, find y for x 0.1, 0.2, 0.3, given that 9 dy/dx =
XY+Y2, y(0) = | . Continue the solution at x 0.4 using Milne's method.

PART C

a. Explain i) Collocation method and ii) Galerkin's method 3 b. Solve the boundary value
problem y' -64y + 10 0 with Y(9)=y(1)=Oby the finite 9 difference method. Take and find
y(0.5).
a. Explain Schmidt method for solving partial differential equations. 3
b. Solve the Poisson's equation uxx+ uyy = -81xy, 01 2<%<1, 044 Given thatu(0,y)=09
५८11 00, u(x, | 100 and ೧51/3

a.Solve the boundary value problem uxx under the conditions u(0,t) = u(I,t) and 12 u(x,O)
sin നാ Of-xSI using Schmidt method (Take ॥-0.2 and a=0.5)