Question

In: Advanced Math

Obtain an estimate for the value of e by approximating the solution of the following initial...

Obtain an estimate for the value of e by approximating the solution of the following initial value problem at t = 1

y'=y     y0=1    

Use a step size of 0.25. Apply Euler’s Method, the Midpoint Method, and the Improved Euler’s Method in order to approximate the solution to this problem. Calculate the absolute relative true percent error using seven significant figures. Calculate this error for each method and only for the last iteration.

Solutions

Expert Solution


Related Solutions

Approximating Integrals. What value of ? should be used to guarantee that a Midpoint Rule estimate...
Approximating Integrals. What value of ? should be used to guarantee that a Midpoint Rule estimate of ∫ ??2?? 1 0 is accurate to within 0.01?
Solve the following initial value problem, showing all work. Verify the solution you obtain. y^''-2y^'+y=0; y(0)=1,y^'...
Solve the following initial value problem, showing all work. Verify the solution you obtain. y^''-2y^'+y=0; y(0)=1,y^' (0)=-2.
Two coding challenges this week! Part 1: Estimate the value of e. e is defined as  as...
Two coding challenges this week! Part 1: Estimate the value of e. e is defined as  as n goes to infinity. So the larger the value of n, the closer you should get to e. math.e is defined as 2.718281828459045 You'll write a program that uses a while loop to estimate e to within some defined error range, while having a limit on how many iterations it will attempt. Part 2: Palindrome detection A palindrome is a string that is the...
Find the solution to the following initial value problem y' -y = t - sint +...
Find the solution to the following initial value problem y' -y = t - sint + e^(2t); y(0) = 0
Find the solution of the following initial value problem. y''' + y'' + y' + y...
Find the solution of the following initial value problem. y''' + y'' + y' + y = e^-t + 4cost ; y(0)= 0, y'(0)= -1, y''(0)= 0
use the method of order two to approximate the solution to the following initial value problem...
use the method of order two to approximate the solution to the following initial value problem y'=e^(t-y),0<=t<=1, y(0)=1, with h=0.5
Compute, by Euler’s method, an approximate solution to the following initial value problem for h =...
Compute, by Euler’s method, an approximate solution to the following initial value problem for h = 1/8 : y’ = t − y , y(0) = 2 ; y(t) = 3e^(−t) + t − 1 . Find the maximum error over [0, 1] interval.
Estimate ∫^−3 −5 ?^2+5? ?? using midpoints for ?=4n=4 approximating rectangles.
  Estimate ∫^−3 −5 ?^2+5? ?? using midpoints for ?=4n=4 approximating rectangles. ∫^−3 −5 ?^2+5? ?? is approximately Estimate ∫^3 2 2/? ?? using right endpoints for ?=3 approximating rectangles. ∫^3 2 2/? ?? is approximately Consider the integral ∫102(4?^2+2?+6)?? (a) Find the approximation for this integral using left endpoints and ?=4 ?4= (b) Find the approximation for this same integral, using right endpoints and ?=4 ?4=
Determine the solution of the following initial boundary-value problem using the method of separation of Variables...
Determine the solution of the following initial boundary-value problem using the method of separation of Variables Uxx=4Utt 0<x<Pi t>0 U(x,0)=sinx 0<=x<Pi Ut(x,0)=x 0<=x<Pi U(0,t)=0 t>=0 U(pi,t)=0 t>=0
Use the method of Undetermined Coefficients to find the solution of the initial value value problem:...
Use the method of Undetermined Coefficients to find the solution of the initial value value problem: y'' + 8y' + 20y = 9cos(2t) - 18e-4t, y(0) = 5. y'(0) = 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT