Answer to Question #60693 in Math for esita

Question

9. a) The following table of values of )x(f is given

Find )2.0( f′ using an h(0 )
2
method (using all the three values.) (2)
b) Evaluate by Simpson’s one-third rule an approximate value of ∫
+
1
0
sin x cos x dx using 7
ordinates. (4)
c) Determine the value of the integral
∫
= +
1
0
2 2/1
I 1(x x ) dx
by composite trapezoidal rule with 3 and 5 ordinates. Improve the result by using
extrapolation technique. (4)
10. a) Find the solution of the difference equation yk+2 − 4yk+1 + 4yk = ;0 k = ,1,0 K. Also find
the particular solution when 1 y0 = and 6 y1 = . (2)
b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )2.4(y . (2)
c) Solve the IVP
y 1 y , )0(y 0
2
′ = + =
using classical R-K method of h(0 )
4
. Find )4.0(y taking h = 2.0 . Compare the solution
obtained with the exact solution and find the error. (6)
x 0.2 0.3 0.4
f(x) 1.2214 1.3499 1.4918