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Approximate the solution to the above initial value problem

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Reference no: EM13574241

dy/dt = te3t - 2y, 0 ≤ t ≤ 1, y(0) = 0

Approximate the solution to the above initial value problem using

(a) Modified-Euler Method

(b) Midpoint Method

(c) Heun's Method

(d) 4-stage Runge-Kutta Method

with a time step of h = 0.1. For each method, tabulate the approximate solution and the error at each time step using the exact solution to this problem

y(t) = 1/5 te3t -1/25 e3t +1/25e-2t

Plot the approximate solutions and the exact function for comparison. In another graph, plot the error distributions. Note that you may need to give a separate plot for the error of 4-stage Runge-Kutta scheme to see the trend in a larger scale.

Reference no: EM13574241

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