# Write a user-defined function y = AB_3(f,x,y 0 ) that solves an IVP y? = f(x,y), y(x 0 ) = y=…

Write a user-defined function y = AB_3(f,x,y0) that solves an IVP y′ = f(x,y), y(x0) = y= using the third-order Adams–Bash forth method. Solve the IVP in Problem 46 by executing AB_3. Compare the value of y3 with that obtained in Problem 46.

Problem 46

Consider the IVP

a. Using RK4, find an estimate for y1, y2, and y3.

b. Using y0 (initial condition), and y1 and y2 from (a), apply the third order Adams–Bash forth formula to find y3.

c. Compare the relative errors associated with the y3 estimates found in (a) and (b), and comment. The exact solution is

Problem 46

Consider the IVP

a. Using RK4, find an estimate for y1, y2, and y3.

b. Using y0 (initial condition), and y1 and y2 from (a), apply the third order Adams–Bash forth formula to find y3.

c. Compare the relative errors associated with the y3 estimates found in (a) and (b), and comment. The exact solution is