find through experimentation the largest value of Δt where the exact solution and the numerical solution by Heun’s method cannot be distinguished visually.

a) A second-order Runge-Kutta method, also known has Heun’s method, is derived in Sect. 8.4.5. Make a function ode_Heun(f, U_0, dt, T) (as a counterpart to ode_FE(f, U_0, dt, T) in ode_FE.py) for solving a scalar ODE problem u
= f (u, t), u(0) = U0, t ∈ (0, T ], with this method using a time step size Δt.

b) Solve the simple ODE problem u
= u, u(0) = 1, by the ode_Heun and the ode_FE function. Make a plot that compares Heun’s method and the Forward Euler method with the exact solution u(t) = et for t ∈ [0, 6]. Use a time step Δt = 0.5.

c) For the case in b), find through experimentation the largest value of Δt where the exact solution and the numerical solution by Heun’s method cannot be distinguished visually. It is of interest to see how far off the curve the Forward Euler method is when Heun’s method can be regarded as “exact” (for visual purposes).

find the cost of your paper

Complete independent research and review two (2) to three (3) online end-user license agreements.

Complete independent research and review two (2) to three (3) online end-user license agreements. Compare and contrast each EULA with each other. In your response, please consider the following: ·….

Write a SQL query that identifies the number of prescriptions grouped by drug name.

ALY6030 Final Project Assignment – Pharmacy Claims Due End of Week 6 Background: The excel file “ALY 6030 Final Project Data Set.xlsx” contains sample pharmacy claims for made-up members of….

Create a JavaFX program to allow a user to query the Northwind database.

Create a JavaFX program to allow a user to query the Northwind database. You should be able to perform the following functionality using the program:   Print order total (not….