Derive the computational scheme and show that (contrary to the Forward Euler scheme) you have to solve a nonlinear algebraic equation for each time step when using this scheme.

1.Let y be a scalar function of time t and consider the nonlinear ODE y + y = ty3, t ∈ (0, 4), y(0) = 1 2 . a) Assume you want to solve this ODE numerically by the Backward Euler method. Derive the computational scheme and show that (contrary to the Forward Euler scheme) you have to solve a nonlinear algebraic equation for each time step when using this scheme. b) Implement the scheme in a program that also solves the ODE by a Forward Euler method. With Backward Euler, use Newton’s method to solve the algebraic equation. As your initial guess, you have one good alternative, which one? Let your program plot the two numerical solutions together with the exact solution, which is known (e.g., from Wolfram Alpha) to be y(t) = √ 2 √ 7e2t + 2t + 1

2.Assume that the initial condition on u is nonzero in the finite difference method from Sect. 8.4.12: u
(0) = V0. Derive the special formula for u1 in this case. Filename: ic_with_V_0.pdf.

find the cost of your paper

Propose (or illustrate) a database solution enabling service representatives to identify the most important customers so that they could receive priority service.

For this week’s assignment, you will propose (or illustrate) a database solution enabling service representatives to identify the most important customers so that they could receive priority service. You will use….

Description of the how the software selection criteria (and which ones) were chosen for your company

Integrated Learning Project Assignment Instructions Overview The integrated learning assignment is a series of 6 assignments and a final course consolidated submission. All assignments and the compilation of the final….

How can Layla use JavaScript custom objects to create the Customer List feature for the Web site?

Layla just got hired as the Web developer for a small business called Axe Grinders, which sells and repairs guitars and amps. The aging rock 'n' rollers who own Axe….