Consider the following initial value problem y = -5y + 5++ 2t, Ostsi, y(0) = 1/3,...
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)
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Using the fourth order Runge-Kutta method (KK4 to solve a first order initial value problem NOTE: This assignment is to be completed using MATLAB, and your final results including the corresponding M- iles shonma ac Given the first order initial value problem with h-time step size (i.e. ti = to + ih), then the following formula computes an approximate solution to (): i vit), where y(ti) - true value (ezact solution), (t)-f(t, v), vto)...
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
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Question 1: Given the initial-value problem 12-21 0 <1 <1, y(0) = 1, 12+10 with exact solution v(t) = 2t +1 t2 + 1 a. Use Euler's method with h = 0.1 to approximate the solution of y b. Calculate the error bound and compare the actual error at each step to the error bound. c. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual value...
Given the initial-value problem y'=2-2tyt2+1, 0 ≤t≤1, y0=1 With exact solution yt= 2t+1t2+1 Using MATLAB use Euler’s method with h = 0.1 to approximate the solution of y
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real parameter a. Verify that y(t) = e-kt (14) is the exact solution of the BVP. b. Use the function mybvp() from the previous problem with h -0.1 and k -10, to solve the BVP by the Finite Difference Method. Plot, on the same axes, the numerical and exact solution. c. Using a log-log plot, graph the maximum error as a function...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
Problem 1. Consider the following initial value problem: d = 3t+y+1, (0) - 4. Denote the solution of the initial value problem by 9 (a) Use the method for solving linear differential equations from Chapter 1 (using an integrating factor) to find the exact solution to the initial value problem. (b) Use the Improved Euler's method to estimate 9(0.2) using a step size of At -0.1 in other words, using two steps). Answer this by filling out a table like...
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
5.Solve the initial value problem y" +5y' +6y-g(t), y(0) 0,(0) 2, where (t)-t 1<t<5,. 1, 5 < t. Then sketch the graph of the solution. (Use technologies. Be sure the graph is neat.) Sec. 7.6.39]