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 appr...
Consider the initial value problem below to answer to following. a) Find the approximations to y(0.2) and y(0.4) using Euler's method with time steps of At 0.2, 0.1, 0.05, and 0.025 b) Using the exact solution given, compute the errors in the Euler approximations at t 0.2 and t 0.4. 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 0.2 and t...
I. Use Euler's method with step size h = 0.1 to numerically solve the initial value problem y,--2ty+y2, y(0) 1 on the interval 0 < t 2. Compare your approximations with the exact solution. I. Use Euler's method with step size h = 0.1 to numerically solve the initial value problem y,--2ty+y2, y(0) 1 on the interval 0
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 a step size h = 0.1 to approximate y(0.0), y(0.1), y(0.2), y(0.3), y(0.4), y(0.5) where y(x) is the solution of the initial-value problem ay = - y2 cos x, y(0) = 1. (b) Find and compute the exact value of y(0.5). dx
Consider the initial-value problem yl =0.3y y(3) = 0.2 (a) Use Euler's method to estimate y (-2with step size h 0.5 Give your approximation for y (-2)with a precision of ±0.01 y(2) Number (b) Use Euler's method to estimate y (-2)with step size h = 0.25 Give your approximation for y (-2)with a precision of ±0.01 y (-2) Number Consider the initial-value problem yl =0.3y y(3) = 0.2 (a) Use Euler's method to estimate y (-2with step size h 0.5...
(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,...
(d) This part of question is concerned the use the Euler's method to solve the following initial-value problem dy dx4ar (i) Without using computer software, use Euler's method (described in Unit 2) with step size of 2, to find an approximate value y(2) of the given initial-value problem. Give your approximation to six decimal places. Clearly show all your working 6 (ii) Use Mathcad worksheet Έυ1er's method, associated with Unit 2 to computer the MATHCAD estimate solutions and absolute errors...
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...
Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem d2 dt Obtain your solution with (a) Euler's method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y- cos(3t). Note: show the hand calculations for t-0.1 and 0.2, for remaining work use the MATLAB files provided in the lectures Problem...
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...