In this problem, you are going to look at how the accuracy of the solution of an ODE depends on the time step. Consider the integration of the differential equation

over the domain x ∈ [0, 1] with the initial condition y(0) = 0. Write a program that uses implicit Euler to compute the value of y(1) when the number of time steps n = 10, 20, . . . , 1000. In other words, the first calculation divides the domain from x = 0 to x = 1 into ten intervals and so forth. As you are marching the solution forward in time, use a zero-order continuation method to produce the initial guess for Newton’s method. Within Newton’s method, your convergence criteria should be |f (y^(k)_i+1)|

Transcribed Image Text:

dy = dx = sin(x) cos(лy) exp(-[x² + y²)]