Numerical Methods - Study Mode
[#36] During the numerical solution of a first order differential equation using Euler method with step size h, the local truncation error is of order of
Correct Answer
(A) h 2
[#37] With respect to the numerical evaluation of the definite integral $${ ext{K}} = int_{ ext{a}}^{ ext{b}} {{{ ext{x}}^2}{ ext{dx,}}} $$ xa0 where a and b are given, which of the following statements is/are TRUE? I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral. II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
Correct Answer
(C) Both I and II
[#38] The following equation needs to be numerically solved using the Newton-Raphson method. x 3 + 4x - 9 = 0. The iterative equation for this purpose is (k indicates the iteration level)
Correct Answer
(A) $${{ ext{x}}_{{ ext{k}} + 1}} = frac{{2{ ext{x}}_{ ext{k}}^3 + 9}}{{3{ ext{x}}_{ ext{k}}^2 + 4}}$$
[#39] Newton-Raphson method is used to compute a root of the equation x 2 - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is
Correct Answer
(D) 3.607
[#40] Identify the Newton-Raphson iteration scheme for finding the square root of 2.
Correct Answer
(A) $${{ ext{x}}_{{ ext{n}} + 1}} = frac{1}{2}left( {{{ ext{x}}_{ ext{n}}} + frac{2}{{{{ ext{x}}_{ ext{n}}}}}}
ight)$$