Assignment-2
October, 2021
510
Numerical Computing
1- Given the data points
x1 2 3 4 5
y 13 15 12 9 13
(a) determine the natural cubic spline interpolate at x = 3.4.
(b) determine y’ and y’’ at x = 3 and x = 3.4.
3
(c) determine ∫1 𝑓(𝑥)𝑑𝑥
𝑑𝑖
2- The differential equations governing the loop current i of the electric circuit are 𝐿 𝑑𝑡 +
𝑅𝑖 = 𝐸(𝑡). Use R = 1.0 ohm, L = 2H, and E(t) = Sint. Where 0 ≤ 𝑡 ≤ 10, 𝑎𝑛𝑑 𝑖(0) =
0.5𝐴. Compute i(10) with h = 2.5 using following algorithms.
(a) Modified Euler Method.
(b) RK Method
(c) Adams Method
3- Use Galerikin’s technique to solve 𝑦 ′′ = 3𝑥 + 1, 𝑦(1) = 1.5 𝑎𝑛𝑑 𝑦(2) = 2 using a
cubic polynomial approximation.
4- Use Rayleigh-Ritz method to solve q-3.