MATLAB question:

Develop code that will implement Euler's method for a first-order differential equation defined in a file myode. Use the same conventions as the inbuilt Matlab functions (e.g., ode45 - if your function is called euler, I should be able to run it as [t,y] = euler(@myode,tspan,y0). Your method should refine the step size until you have achieved convergence.

As a test function, use dx/dt = -2x with x(0) = 10 . Integrate over t = [0 4].

Modify your Euler's code to implement a general second-order Runge-Kutta method. Use the same test function as above.

Solve the test function analytically. For Euler's and Heun's methods, make a plot showing how the absolute true error varies with step-size (you need to solve the problem by hand to obtain the true error). Do your results agree with your expectations?