Differential EquationsI need help with this small project, I've got the other 3 problemsdone but the provided pictures are the instructions and numbers1,2,3 from page 136A screenshot of an excel sheet is fine, no need to use any CSlanguage
Differential Equations I Need Help With This Small Project I Ve Got The Other 3 Problems Done But The Provided Pictures 1 (27.2 KiB) Viewed 51 times
Differential Equations I Need Help With This Small Project I Ve Got The Other 3 Problems Done But The Provided Pictures 2 (110.62 KiB) Viewed 51 times
For this project you will either write a program or use Excel to implement Euler's Method, Improved Euler's Method, and the Runge-Kutta Method. For each of the four problems, you will determine how many subintervals you need in order to compute the value of y(1) using each method accurate to 9 decimal places. The first three problems can be found on pg 117, 126 and 136 numbers 1, 2, and 3 (same three problems on each page, but with a different method each time). In addition to the instructions given, solve the initial value problems explicitly. The fourth differential equation to solve is as follows: dy dx 1 =10y-e**, y(0) = — 11 Find y(1) as before. For each of the problems, discuss how the methods compared and any issues that arose and possible causes for them. State clearly how many subintervals were needed to compute y(1) accurately to nine decimal places.
Famous Numbers Revisited, One Last Time The following problems describe the numbers e≈ 2.71828182846, In 2≈ 0.69314718056, and ~ 3.14159265359 as specific values of certain initial value problems. In each case, apply the Runge- Kutta method with n = 10, 20, 40, ... subintervals (doubling n each time). How many subintervals are needed to obtain-twice in succession-the correct value of the target number rounded to nine decimal places? 1. The number e = y(1), where y(x) is the solution of the initial value problem dy/dx = y, y(0) = 1. 2. The number In 2 = y(2), where y(x) is the solution of the initial value problem 1/x, y(1) = 0. dy/dx = 3. The number = y(1), where y(x) is the solution of the initial value problem dy/dx = 4/(1+x²), y(0) = 0.
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!