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00000MA486052002

Minimize f(A) = 242 + =

1, € = 0.04. (Three iterations)

using Newton's direct root method starting point 41 = (7)

: ⋅ ಜ್‌ ಪ್‌ (8)
rom the following data, obtain — and - > at x = 500

PART ட
Answer any two full questions, each carries 20 marks

Minimise f(x, 9) = x” + 2y? starting from the point 8 using Fletcher-Reeve’s (14)
method.
Minimise f(x,,x2) = 6x," + 2222 - 6122 - 21- 2 ‏جد‎ starting from the point (6)
X, = (0 using Newton’s method.

0
Solve the equation டி = Uy, subject to the conditions u(x,0) = 511172,0 < ८ < (10)
1,u(0,t) = u(1,t) = 0. compute wu for two time levels by taking h = sk = +

using Crank-Nicolson Method.
Solve ಹ + Uyy = 0 over the square mesh with boundary values as shown in the (10)

figure. Assuming ८4 = 0.75, iterate till the mesh values are correct up to two

decimal places using Gauss- Seidel Method.

1 2 2 2
0 5 2
0 | |, | a
0 0 0 > न
Minimise f(x1,x2) = 51 —X2 + 2212 + 22122 + x2” starting from the point (10)

1 = (0) using Univariate method. (Two iterations, take ടെ 0.01, ).
Evaluate the pivotal values of the equation ४६६ = 16u,, taking Ax = 1 up to (10)

t = 1.25. The boundary conditions are u(0,t) = u(5,t) = 0,5" (x, 0) = 0 and
initial condition u(x, 0) = x2(5— ൧.

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