PART 8

Obtain the cubic spline approximation of the given data and find yo .5) and $" (3).
೫: 2 3 4

s 11 8

5. Given that
x 4 4.2 44 4.6 4.8 5.0 5.2

logx : 1.3863 1.4351 1.4816 1.5261 1.5686 1.6094 1.6487

Evaluate L 5.2 logx dx by Simpson's 1/3-rule, Simpson's 3/8-rule and Weddle's rule.
Also find the error in each case.

. Solve the following by Euler's modified method x + siny,
/(0)=1,compute (0.2) and y(O.4) with h=O.2

PART C

7. Determine the values of y at the pivotal points of the interval (0,1) if y satisfies the
boundary value problem y' +81 y=81 x2, YO)}=y(1)=y"(0)=y’’(1 )=0.Take n=3

8. a)Explain Schmidt method for solving partial differential equations. (3 marks)

b)Solve the Poisson's equation uxx+ u = -81xy, for 0u(t. y)=100, u(x, and h=1/3 (9 marks)

Find the values of u(x,t) satisfying the parabolic equation ut = 4uu under the conditions
u(8,t)=Oand —http:8www.ktuonline.com and j/8:
४70, 1,2....5.