Question

In: Advanced Math

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

Solutions

Expert Solution

Solution: Given Initial value problem is

with h=0.5.

Let

The Taylor's method of order two for general initial value problem (*) is given by

where h is small.

Therefore,The Taylor's method of order two for general initial value problem (i) is given by

With , equation (**) becomes

Therefore, with , we have

Therefore and .

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Use Eulers method to find approximate values of the solution of the given initial value problem...

Use Eulers method to find approximate values of the solution of the given initial value problem at T=0.5 with h=0.1. 12. y'=y(3-ty) y(0)=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.

Use power series approximations method to approximate the solution of the initial value problem: y"− (1+...

Use power series approximations method to approximate the solution of the initial value problem: y"− (1+ x) y = 0 y(0) = 1 y'(0) = 2 (Write all the terms up to the power ). x^4

Use eulers Method with step size h=.01 to approximate the solution to the initial value problem...

Use eulers Method with step size h=.01 to approximate the solution to the initial value problem y'=2x-y^2, y(6)=0 at the points x=6.1, 6.2, 6.3, 6.4, 6.5

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

Problem Four (12 Marks) Use Runge Kutta method of order four to approximate the solution of...

Problem Four Use Runge Kutta method of order four to approximate the solution of the initial value problem ?′ + 2? = ??3?, 0 ≤ ? ≤ 1, ?(0) = 0, ???ℎ ℎ = 0.5 Hint: Compute ?(0.5) ??? ?(1)

Use the method of steepest ascent to approximate the optimal solution to the following problem: max⁡...

Use the method of steepest ascent to approximate the optimal solution to the following problem: max⁡ z=-(x1-2)^2-x1-(x2)^2 . Begin at the point(2.5,1.5) (p.s. The answer already exists on the Chegg.Study website is incorrect)

Use the finite difference method and the indicated value of n to approximate the solution of...

Use the finite difference method and the indicated value of n to approximate the solution of the given boundary-value problem. (Round your answers to four decimal places.) x2y'' + 3xy' + 5y = 0, y(1) = 6, y(2) = 0; n = 8 x y 1.000 ? 1.125 ? 1.250 ? 1.375 ? 1.500 ? 1.625 ? 1.750 ? 1.875 ? 2.000 ?

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

Calculate the Euler method approximation to the solution of the initial value problem at the given...

Calculate the Euler method approximation to the solution of the initial value problem at the given x-values. Compare your results to the exact solution at these x-values. y' = y+y^2; y(1) = -1, x = 1.2, 1.4, 1.6, 1.8

Subjects