exam 11 (50).pdf - Question Given the initial conditions y(0 = 1 and y(0 = 0 solve the following initial-value problem from t = 0 to 4 Obtain your

exam 11 (50).pdf - Question Given the initial conditions...

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Question: Given the initial conditions, y(0) = 1 and y'(0) = 0, solve the following initial-value problem from t = 0 to 4: Obtain your solutions with (a) Euler’s method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y = cos 2t. Answer : The second order differential equation can be expressed as system of two first order ODEs, that is, (a) The Euler method is given as , here the variables have usual meaning. The differential equation is evaluated using Euler’s method with step size and the results of few steps is shown in the table given below:
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(b) It is required to evaluate the given equation using fourth order RK method with . Evaluate the slope at the beginning of the interval Use this value to compute a value of and
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