1.) Apply the classical Runge-Kutta method to solve the following initial value
ID: 3775379 • Letter: 1
Question
1.) Apply the classical Runge-Kutta method to solve the following initial value problem y'=1+y given y(0)=1 and the step size h=0.1. Verify solution using MATLAB. Plot the solutions obtained by using ode45 and dsolve. Compare the graphs and provide an explanation.
Type as much of your answer as possible in the space below. If you need to reference your Problem Work for this assessment, type ‘See Problem Work’ at that point in your answer.
2.) provide a table of values comparing the exact y, approximate y evaluated using the Euler method and the error for each step given y'=1+y, y(0)=1 and h=0.1. Type as much of your answer as possible in the space below. If you need to reference your Problem Work for this assessment, type
‘See Problem Work’ at that point in your answer.
Explanation / Answer
Apply the classical Runge-Kutta method to solve the following initial value problem y'=1+y given y(0)=1 and the step size h=0.1. Verify solution using MATLAB. Plot the solutions obtained by using ode45 and dsolve. Compare the graphs and provide an explanation.
Type as much of your answer as possible in the space below. If you need to reference your Problem Work for this assessment, type ‘See Problem Work’ at that point in your answer.
2.) provide a table of values comparing the exact y, approximate y evaluated using the Euler method and the error for each step given y'=1+y, y(0)=1 and h=0.1. Type as much of your answer as possible in the space below. If you need to reference your Problem Work for this assessment, type
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