Consider the initial value problem below to answer to following. a) Find the approximations to y(0.2)...
Consider the initial value problem below to answer to following. a) Find the approximations to y(0.3) and y(0.6) using Euler's method with time steps of At 0.3, 0.15, 0.075, and 0.0375 b) Using the exact solution given, compute the errors in the Euler approximations at t 0.3 and t 0.6. c) Which time step results in the more accurate approximation? Explain your observations. d) In general, how does halving the time step affect the error at t 0.3 and t...
This Question: 1 pt Consider the initial value problem below to answer to following. a) Approximate the value of y(T) using Euler's method with the given time step on the interval [o.TI b) Using the exact solution given, find the error in the approximation to y(T) (only at the right endpoint of the interval) c) Repeating parts d) Compare the errors in the approximations to y(T) a and b using half the time step used in those calculations, again find...
Please help with all the parts to the question Consider the initial value problem y (t)-(o)-2. a. Use Euler's method with At-0.1 to compute approximations to y(0.1) and y(0.2) b. Use Euler's method with Δ-0.05 to compute approximations to y(0.1) and y(02) 4 C. The exact solution of this initial value problem is y·71+4, for t>--Compute the errors on the approximations to y(0.2) found in parts (a) and (b). Which approximation gives the smaller error? a. y(0.1)s (Type an integer...
a use Euler's method with each of the following step sizes to estimate the value of y 0.4 where y is the solution of the initial value problem y -y, y 0 3 カー0.4 0.4) (i) y10.4) (in) h= 0.1 b we know that the exact solution of the initial value problem n part a s yー3e ra , as accurately as you can the graph of y e r 4 together with the Euler approximations using the step sizes...
(a) Use Euler's method with each of the following step sizes to estimate the value of y(0.8), where y is the solution of the initial-value problem y' = y, y(0) = 3. (i) h = 0.8 y(0.8) = (ii) h = 0.4 y(0.8) = (iii) h = 0.2 y(0.8) = (b) We know that the exact solution of the initial-value problem in part (a) is y = 3ex. Draw, as accurately as you can, the graph of y = 3ex,...
Need Help with solving for answers in Part C and Part D! Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0,3, and 0.4, (A COmputer algebra system is recommended. Round your answers to five decimal places.) (a) Use the Euler method with0.05 (0.11.5875 y(0.2)2.12747 y(0.3)2.62455 y(0.4)3.0829 (b) Use the Euler method with h0.025 y(0.1)1.58156 y(0.2)2.11675 (o.3)261 y(0.4)3.0654 (c) Use the backward Euler method with h 0.05 (0.2) y(0.3) y(0.4) (d) Use...
Please explain and provide answers for parts a-c. Please round to five decimal places for all. Thanks! omework: Week 09 Section 8.2 Homework 9 of 10 (10 complee) core: 0.2 of 1 pt 8.2.33 Consider the initial value problem below to answer to following a) Approximate the value of y(T) using Euler's method with the given time step on the interval [0,TI. b) Using the exact solution given, find the error in the approximation to y(T) (only at the right...
Is it possible to do this without matlab? 3In modelling the velocity y of a chain slipping off a horizontal platform, the differential equation y'- 10/y - y/x is derived. Suppose the initial condition is y (1)1 (a) Euler's method for solving y-f(x,y), y(XO-yo, is given byYn+1-yn+hf(xn,Yn) where h is a fixed stepsize, xnxo nh, and yn ~y(x). Apply one step of Euler's method to the initial value problem given above (b) Apply one step of the improved Euler method...
Complete using MatLab 1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
VOX) + Consider the initial value problem y' - 2x - 3y + 1, y(1) 9. The analytic solution is 1 2 74 + -3x - 1) 3 9 (a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method is used. (b) Find a bound for the local truncation error in each step ith-0.1 is used to approximate y(1.5). (Proceed as in Example 1 of Section 6.1.) (c) Approximate y(1.5)...