Professor Kate Poirier | OL67 | Fall 2020

Due Sunday, October 11

Numerical methods provide us a way to approximate solutions of initial value problems without actually having to solve them. In Chapter 3, we see three of these methods for initial value problems of the form , :

• Euler’s method
• Improved Euler’s method
• Runge-Kutta method

For Part 1 of Project 2, you will create your own calculator to approximate the solution of one initial value problem using all four of these methods, each with different step sizes. You will not perform your calculations by hand; instead you should use spreadsheet software like Excel or Google Sheets. You may write your own computer program instead of using a spreadsheet if you prefer.

Here is an example of the type of spreadsheet you will create (though this spreadsheet does not conform to all the instructions below).

Contents

## Instructions

This is not a group project. You may help each other, but each student must submit their own work.

1. Choose one of the problems below and submit a comment on this post with the number corresponding to your choice (no more than three people may choose the same problem).
2. Solve the problem using each of the three methods. Use a spreadsheet or write your own computer program to perform these calculations. If using a spreadsheet, include calculations for the different methods on different sheets. Make sure to organize your work and indicate clearly the calculations for different step sizes. Your solution must also display any intermediate values found while carrying out each method:
• Euler’s Method: display the slope as well as and values at each stage,
• Improved Euler’s: also display the values of and at each stage
• Runge-Kutta: also display the values of , , and at each stage
• You can display other values as well, if you wish.

## Problem choices

1. Use step sizes to find approximate values of the solution of the initial value problem at . 2. Use step sizes to find approximate values of the solution of the initial value problem at . 3. Use step sizes to find approximate values of the solution of the initial value problem at . 4. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  5. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  6. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  7. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  8. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  9. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  10. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  11. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  12. Use step sizes to find approximate values of the solution of the initial value problem at equally spaced points in the interval  • functioning solutions for all three methods,
• all appropriate intermediate values at each stage,
• answers that are correct up to 5 decimal places at each stage,
• work that is clearly labelled and organized.

## Technical help

The Atrium Learning Center offers free self-paced instruction in Microsoft Office (which includes Excel). Information is here:

1. Richard Li

Number 5

2. Raisa Ratri

Number 10

3. Sheyla Criollo

number 5

4. Jennifer Agudelo

Number 10

5. Oscar

2

6. Sierra Morales

Problem 1

7. Brian Enriquez

Problem 8

8. Jian Hui

Number 5

9. Ryjll Morris

Number 5

• Ryjll Morris

Number 10 sorry

10. julio dominguez

Number 1

11. Kelon McKoy

Problem 1

12. Jason Zhu

Number 2

13. Jason Zhu

Number 2

14. Wilfrido V.

Number 3

15. aron singh

number 3

16. Omrit P

Number 3

17. Ariel Itshaik

number 4

18. Dief

Problem 2

19. Dief

Sorry professor, I did 10 rather than 2

20. Trevon

Problem #3

21. Trevon

Problem # 4 actually

22. Tushar Shorma

number 10

23. Mushrat

no: 12

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