Question

B1. Consider the initial value problem given by y 0 (t) = sin2 (y) ln(t +...

B1. Consider the initial value problem given by y 0 (t) = sin2 (y) ln(t + 1), with the initial condition y(0) = 1. Perform three iterations of Midpoint Method, using a step size of h = 1 3 , to obtain an estimate of the solution at t = 1.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given the initial value problem: y'=6√(t+y),  y(0)=1 Use Euler's method with step size h = 0.1 to...
Given the initial value problem: y'=6√(t+y),  y(0)=1 Use Euler's method with step size h = 0.1 to estimate: y(0.1) = y(0.2) =
Given : dy/dt = -100000y + 99999 e^(-t) a. If y(0)=0 use the explicit Euler method...
Given : dy/dt = -100000y + 99999 e^(-t) a. If y(0)=0 use the explicit Euler method to obtain a solution using a step size of 0.1. Carry out 2 iterations. What do you notice? b. Estimate the minimum step size required to maintain stability using the explicit Euler method. b. Repeat the problem using the implicit Euler method to obtain a solution from t=0 to 2 using a step size of 0.1.
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact)...
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact) solution y(t). (a) Verify that the solution of the initial value problem is y(t) = 1/(3e^(-t) − t + 1) and evaluate y(1) to at least four decimal places. (b) Use Euler’s method to approximate y(1), using a step size of h = 0.5, and evaluate the difference between y(1) and the Euler’s method approximation. (c) Use MATLAB to implement Euler’s method with each...
Consider the following initial value problem: dy/dt = -3 - 2 * t2,       y(0) = 2...
Consider the following initial value problem: dy/dt = -3 - 2 * t2,       y(0) = 2 With the use of Euler's method, we would like to find an approximate solution with the step size h = 0.05 . What is the approximation of y (0.2)?  
Consider the initial value problem: y' - (7/2)y = 7t + 2e^t Initial condition: y(0) =...
Consider the initial value problem: y' - (7/2)y = 7t + 2e^t Initial condition: y(0) = y0 a) Find the value of y0 that separates solutions that grow positively as t → ∞ from those that grow negatively. (A computer algebra system is recommended. Round your answer to three decimal places.) b) How does the solution that corresponds to this critical value of y0 behave as t → ∞? Will the corresponding solution increase without bound, decrease without bound, converge...
for the given initial value problem: (2-t)y' + 2y =(2-t)3(ln(t))    ; y(1) = -2 solve the...
for the given initial value problem: (2-t)y' + 2y =(2-t)3(ln(t))    ; y(1) = -2 solve the initial value problem
4. For the initial-value problem y′(t) = 3 + t − y(t), y(0) = 1: (i)...
4. For the initial-value problem y′(t) = 3 + t − y(t), y(0) = 1: (i) Find approximate values of the solution at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h = 0.1. (ii) Repeat part (i) with h = 0.05. Compare the results with those found in (i). (iii) Find the exact solution y = y(t) and evaluate y(t) at t = 0.1, 0.2, 0.3, and 0.4. Compare these values with the results of...
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to...
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to this initial value problem crosses the x-axis at a point in the interval [0, 1.4]. By experimenting with the improved Euler's method subroutine, determine this point to two decimal points.
Find the solution of the given initial value problem: y " + y = f(t); y(0)...
Find the solution of the given initial value problem: y " + y = f(t); y(0) = 6, y' (0) = 3 where f(t) = 1, 0 ≤ t < π 2 0, π 2 ≤ t < ∞
Consider the initial value problem y' + 5 4 y = 1 − t 5 ,    y(0)...
Consider the initial value problem y' + 5 4 y = 1 − t 5 ,    y(0) = y0. Find the value of y0 for which the solution touches, but does not cross, the t-axis. (A computer algebra system is recommended. Round your answer to three decimal places.) y0 =
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT