2. Use the Taylor's method of order two to approximate the solution to the following initial-value problem y's et-y,0 < t < 1, y (0)-1, with h-0.5 2. Use the Taylor's method...
Use Taylor's method of order two to approximate the solutions for each of the following initial-value problems. c. y'= -y + ty1/2, 25t<3, y(2) = 2, with h = 0.25
Use Taylor's second order method to approximate the solution. y'=-5y+5t^(2)+2t, 0 ≤ t ≤ 1, y(0) = 1/3,with h = 0.1 Also, compare relative errors if the actual solution is: y=t^(2) + 1/3 * e^(-5t)
Problem 1 Use Euler's method with step size h = 0.5 to approximate the solution of the IVP. 2 dy ev dt t 1-t-2, y(1) = 0. Problem 2 Consider the IVP: dy dt (a) Use Euler's method with step size h0.25 to approximate y(0.5) b) Find the exact solution of the IV P c) Find the maximum error in approximating y(0.5) by y2 (d) Calculate the actual absolute error in approximating y(0.5) by /2. Problem 1 Use Euler's method...
Use the modified Euler method to find approximate solution of the following initial- value problem y' -Sy + 16t + 2, ost-1, y(0)-2. Write down the scheme and find the approximate values for h 0.2. Don't use the code.
1. Consider the following initial-value problem. s y' = e(1+B)t In(1 + y2), 0<t<1 y (0) = a +1 a) b) t=0.5. Determine the existence and uniqueness of the solution. Use Euler's method with h = 0.25 to approximate the solution at
.α=2 β=2 1. Consider the following initial-value problem. y' = e(1+B)* In(1 + y²), 0<t<1 y (0) = a +1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h=0.25 to approximate the solution at t=0.5. {v=
Apply Euler-trapezoidal predictor-corrector method to the IVP in problem 1 to approximate y(2), by choosing two values of h, for which the iteration converges. (Don't really need to show work or do by hand, MATLAB code will work just as well). 1. For the IVP: y' =ty, y(0) = ) 0t 4 Compare the true solution with the approximate solutions from t = 0 to t 4, with the step size h 0.5, obtained by each of the following methods....
YOUR TEACHER Consider the initial-value problem y = (x + y - 1)?.Y(0) - 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution (Round your answers to four decimal places.) h 0.1 Y(0.5) h 0.05 Y(0.5) actual value Y(0.5) = Need Help? Tuto Tutor
YOUR TEACHER Consider the initial-value problem y = (x + y - 1)?.Y(0) - 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.) 0.1 y(0.5) h 0.05 (0.5) actual value Y(0.5) - Need Help? Tuto Tutor
B=1 1. Consider the following initial value problem. V = n(1 + y²), OSI31 y(0) = 0+1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t=0.5. 2=8