Write a detailed computer program $($using either MATLAB

or PYTHON$)$ for this beam deflection problem $($as in

question no$.3)$ considering the number of discretizations

as $n($where $n$ can be any positive integer$).$

Describe the theoretical formulation for curve fitting $($in

terms of fitting a line$)$ for a two$-$dimensional dataset based

on the least square error approach.

A plate $($positioned in the horizontal plane, assigned with $x$

and $y$ coordinates$)$ is subjected to load vertically, leading to

plate deflection in the vertical direction $($denoted as $w),$

which is represented by the following partial differential

equation:

$\frac{de{l}^{4}w}{del{x}^4}+2\frac{de{l}^{4}w}{del{x}^{2}del{y}^2}+\frac{de{l}^{4}w}{del{y}^4}=10$

It may be noted that $w$ is a function of both $x$ and $y.$

Consider the length of the plate as $12$ m and $9$ m along the

x $-$axis and y $-$axis, respectively. It is necessary to find out

the deflections of the plate at a few locations $($using the

finite difference method$).$ In this regard, the plate can be

discretized $($equally$)$ into sub$-$domains having three $(03)$

numbers of sub$-$divisions along both the $x$ and $y$ directions.

Besides, consider deflection and slope to be zero at the

boundary of the plate.

Write all the equations necessary to evaluate the intended

deflections.