Consider the second-order IVP: t2y''+ty'-4y=-3t , t in [1,3] and y(1)=4 and y'(1)=3
Solve using Modified Euler's Method with h=1, by first transforming into a first-order IVP and solving.
Consider the second-order IVP: t2y''+ty'-4y=-3t , t in [1,3] and y(1)=4 and y'(1)=3 Solve using M...
Consider the IVP y" - 4y' + 4y = 0, y = -2, y'(0) = 1 a. Solve the IVP analytically b. Using step size 0.1, approximate y(0.5) using Euler's Method c. Find the error between the analytic solution and the approximate solution at each step
Use Reduction of Order method to find the second linearly independent solution: t2y``- ty`+y = 0. y1=t
Exercise 1. We are solving the ODE y'=t2y + cos(y), y(1-1, with a time step h 0.1. Calculate y at t-1.1 using (1) Euler's explicit method; (2) Heun's method; (3) the midpoint method (4) RK4. Detail all calculations; present results in a table; show four significant digits Exercise 1. We are solving the ODE y'=t2y + cos(y), y(1-1, with a time step h 0.1. Calculate y at t-1.1 using (1) Euler's explicit method; (2) Heun's method; (3) the midpoint method...
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 =...
. Consider the IVP y'= 1 + y?, y(0) = 0 a. Solve the IVP analytically b. Using step size 0.1, approximate y(0.5) using Euler's Method c. Using step size 0.1, approximate y(0.5) using Euler's Improved Method d. Find the error between the analytic solution and both methods at each step
If Laplace transform method is used to solve the IVP: y"(t) - 4 y'(t) + 4y(t) = 4 cos2t, yO)= 2; y'(O)=5 then the solution is: Select one: y(t) = e2t + sin2t - cos2t y(t)=2e2t + 2te2t_ 1 sin2t y(t) = 2te + cos2t - sin2t
. Consider the IVP: y + 3y = e 3t, y(0) = 1, y(0) = 0 - Solve the IVP using the guess and test method. .Solve the IVP using the general formula for integrating factors. - Solve the IVP using Laplace Transforms. . Verify that your solution satisfies the differential equation (you should get the same solution using Il three methods, so you only need to test it once).
[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...
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.
Solve the initial value problem ty' + 2ty = 3t + 4, y(1)=theta and plot y versus t for t in the interval [1/2., 2] using matlab.