a)

b)

a)

b)

a)

b)

10000CE473122004

PART C
Answer any two full questions, each carries 20 marks.

Derive the Diagonal five point formula and standard five point formula (8)

Solve the Poisson equationV7u = 82८०} for the square mesh u(x,y) = 0 on the (12)

boundary and mesh length equal to 1.(0 = x = 3), (0 < 9 < 3)

Using Crank — Nicolson method, solve Up = Uyy, 0 > xX > 1,t > 0 subject to: (10)
u(x,0) = 100x(1 - x),u(0,t) = 0, ४(1, 6) = 0 for one time step. Take h = 1/4

Form the Taylor series for y(x), find y(0.1) correct to four decimal places if y(x) (10)

isfi dy = ‏سے‎
‎satisfies ~~ ಹೌ +1,y(0) = 1

Find the minimum of f (x) = —1.5x + x" by starting from (0,0) with an initial step of (10)
0.05 using

i) Fixed step size method

ii) accelerated step size method

Explain the steepest descent method (10)

بد ‎मर‏ م

Page 3 of 3