(Answered) Consider the initial value problem ivp yt 3ty y01a

Statistics

Consider the initial value problem (IVP): y'(t) = 3+t+y y(0)=1

a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)?

b) Use the computer (e.g. ODE Architect, ODE Toolkit, or your own program) to approximate y(1) using step sizes of 0.1, 0.05, 0.025 and 0.01. What is the general relationship between the error of the approximation and the step size?

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