Question

(B4). (10 points) Find the degree of precision of the quadrature formula $\int_0^2 f(x) dx = \frac{1}{2}f(0) + \frac{3}{2}f(\frac{4}{3})$. (B5). (15 points) Consider an initial-value problem $\frac{dy}{dt} = -25y + t^2$, $0 < t < 1$, y(0) = 1. Apply the Euler method to find its approximate solution with the step size h = 0.2 (N = 5) via the following steps: (i) Write down the scheme explicitly in terms of $t_i$ and $W_i$. (Do not use $f(t_i, W_i)$ in your final answer.) (ii) Compute all values of $W_i$. (iii) To have an approximate solution without the growth of oscillation, find the range of step size h.

          (B4). (10 points) Find the degree of precision of the quadrature formula
$\int_0^2 f(x) dx = \frac{1}{2}f(0) + \frac{3}{2}f(\frac{4}{3})$.
(B5). (15 points) Consider an initial-value problem
$\frac{dy}{dt} = -25y + t^2$, $0 < t < 1$,
y(0) = 1.
Apply the Euler method to find its approximate solution with the step size h = 0.2 (N = 5)
via the following steps: (i) Write down the scheme explicitly in terms of $t_i$ and $W_i$. (Do not
use $f(t_i, W_i)$ in your final answer.) (ii) Compute all values of $W_i$. (iii) To have an approximate
solution without the growth of oscillation, find the range of step size h.

(B4). (10 points) Find the degree of precision of the quadrature formula
∫0^2 f(x) dx = (1)/(2)f(0) + (3)/(2)f((4)/(3)).
(B5). (15 points) Consider an initial-value problem
(dy)/(dt) = -25y + t^2, 0 < t < 1,
y(0) = 1.
Apply the Euler method to find its approximate solution with the step size h = 0.2 (N = 5)
via the following steps: (i) Write down the scheme explicitly in terms of ti and Wi. (Do not
use f(ti, Wi) in your final answer.) (ii) Compute all values of Wi. (iii) To have an approximate
solution without the growth of oscillation, find the range of step size h.

Added by Agust-N C.

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