Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y,, for the linear first order initial value problem dy = sin x – y with y(0) = 1 dx in the interval 0s xs 2 in four decimal places.
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- Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y10 for the linear first order initial value problem dy/dx = sinx - y with y(0)=1 in the interval 0 ≤ x ≤ 2 in four decimal places.use the cauchy euler method with h=1/m (m integer) to approximate y(3) for the IVP below. ın each case let h-0 (m- inf) and compare the lımıts with the exact values y'=y^2 y(-1)=0Suppose that a numerical method is used to approximate the solution of an initial -value problem over the time inteval [1,5] with 800 uniform time steps. About how many uniform time steps are needed to reduce the global error by a factor of 1/256? a) Runge Kutta method b) Runge- mid point method c) Euler method