Mathematics, 10.02.2020 23:50, habsofarah0

To derive Euler’s method, we truncated the Taylor series expansion of yi+1 at the linear term. We could truncate at the quadratic term instead, giving the so-called Taylor method of order 2. This method approximates yi+1 byωi+1= ωi+ hf(ti,ωi) + h^2/2. df/dt| (ti,ωi)a. For the IVP y'(t)= y^2. e^-t, 0 ≤ t ≤ 1, y(0)= 1, Calculate df/dt. b. By hand, use both Euler's method and the Taylor method of order 2 to approximate y(1) with h=0.5

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To derive Euler’s method, we truncated the Taylor series expansion of yi+1 at the linear term. We co...