$9$:$13$

HW$2\_$NUM.pdf

EETE $4430-$Applied Numerical Analysis

Spring $2024$

Assignment $2$

Due Date: March $9,2024$

Instructor: Dr$.$ Mustafa El$-$Halabi

Instructions: If you must handwrite your homework, please write clearly and legibly. I will not grade homework that are unreadable.

Note: You must justify all your answers. In particular, you will get no credit if you simply write the final answer without any explanation. Only few selected problems will be graded.

Solve the following equation manually using the false$-$position algorithm

$ln(x)+x=0$

starting with the interval $0\mathrm{.}4,0\mathrm{.}8$ and running the algorithm for $3$ iterations.

$2.$ Write a Matlab code $($call the m$-$file FPA$)$that solves the the equation $ln(x)+x=0$ starting with $x_l,x_u.$ The algorithm should ask you to input $x_{\text{I}}$ and $x_u$ and to specify the number of iterations. At the end of every iteration, your code should display the following information $($you decide how you want to display this information$)$ on the command window screen

The solution in iteration $...$ is $...$

Use the code that you have written to find the solution for the equation $ln(x)+x=0$ starting with $0\mathrm{.}4,0\mathrm{.}8$ after running the false$-$position algorithm for $12$ iterations and specify the solution obtained using $6$ significant figures.

Use the code that you have written to find the solution for the equation $ln(x)+x=0$ starting with $0\mathrm{.}1,2$ after running the false$-$position algorithm for $12$ iterations and specify the solution obtained using $6$ significant figures.

$1$