MATLAB PROBLEM #6

Need Help Writing MATLAB Program For Euler, Heun, and Rugna Kutta Methods

Requirements:

1. Write a main function that cycles until user chooses to stop.

2. Have the user choose the method that will be used, e.g. Euler, Heun or RK4.

3. Use any method of your choice to select one of the following functions to be estimated. Also use any method to input the parameters required before calling the chosen function. a. f1 = 10x^4 -6x the derivative of f1 = 2x^5 -3x^2 -5 b. f2 = 28x^6 -15x^4 +6x^2 -1 the derivative of f2 = 4x^7 - 3x^5 +2x^3 - x

4. This main function will then call one of the three embedded functions:

a. Euler

b. Heun

c. RK4

d. For the 3 above embedded functions: i. Input parameters

1. The derivative function as an autonomous function

2. The initial point

3. Number of points

4. Interval width e.g. h

ii. The output should be a 2xn ( number of points) array of x and y

5. Write a fourth embedded function that computes the actual functions points to compare with the selected method chosen. This function will also output a 2xn array.

6. The main function will then output to the command window the 2 arrays of 2xn points for comparison. This is how to can check your work.

( NOT NEEDED) 7. IMPORTANT (10pts) Run each method at least 2 times with the interval width varied by a significant amount. Then write a short paragraph with table, if required, to comment on the effect of accuracy versus interval width.