Q2- Use Taylor's method of order n=2 to estimate y(1.3) when solving the IVP: y' -...
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)
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 of order two to approximate the solution to the following initial-value problem y's et-y,0
Use one iteration of the Euler method to estimate the solution to the IVP at the point t = 0.1. Show your work 1 y' = 3t+ y(0) = 4
please explain each step
4. (Sec. 3.3, #2) Consider the IVP (0)1 Use the Runge-Kutta's method with step size h-0.1 to estimate y(0.1)-
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 = ( y(t). Transform the above IVP to system of first order (a) Let u(t)y(t) and u2(t) IVP of u and u2. (b) Find y(t) by solving the system with h 0.1 (c) Compare the results to the actual solution y(t) = %et - te 2e t - 2.
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 =...
question b please
Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
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 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
1 Consider the IVP: y' = (2y+t)? y(3) = 2 2 The Taylor method of order 2 for this equation is: wo 2 Wit1 = w; +h ( (2w; +t;)? + h2 h3 (4 (2wi+t;)) + 2 3! 2 Fill in the blank to make this a Taylor method of order 3.
[7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP is y(t) = e−t [1] i) Implement Euler’s method and generate an approximate solution of this IVP over the interval [0,2], using stepsize h = 0.1. (The Google sheet posted on LEARN is set up to carry out precisely this task.) Report the resulting approximation of the value y(2). [1] ii) Repeat part (ii), but use stepsize h = 0.05. Describe...