It’s my first post about what i study in my college , it is about solving a system of equations using the two famous numerical methods of Jacobi and Gauss .

This post is not about these numerical methods themselves but it is about their PHP implementation .

This is the code for Jacobi :

<?php
$x = array(
array(0,-(1/3),-(1/3),-(8/3)),
array((1/3),0,-(1/3),(8/3)),
array(-(1/3),(1/3),0,-(8/3))
);
$s = array(
0,0,0
);
echo "<table border='1' style= 'width :90%'><tr>";
echo "<td> k = 0</td><td> 0</td><td> 0</td><td> 0</td></tr>";
for($i=1;$i<=30;$i++){
echo "<tr>";
$s0 = ( $s[0]*$x[0][0]) + ( $s[1]*$x[0][1])+($s[2]*$x[0][2]+$x[0][3]);
$s1 = ($s[0]*$x[1][0]) + ($s[1]*$x[1][1]) + ($s[2]*$x[1][2]+$x[1][3]);
$s2 = ( $s[0]*$x[2][0]) + ($s[1]*$x[2][1]) + ($s[2]*$x[2][2]+$x[2][3]);
$s[0] = $s0;
$s[1] = $s1;
$s[2] = $s2;
echo "<td> k = $i</td><td>".$s[0]."</td><td>".$s[1]."</td><td>".$s[2]."</td></tr>";
//echo $i." :: ".$s[0]." :: ".$s[1]." :: ".$s[2]."<br>";
}
echo "</table>";
?>

And this is the gauss-siedle

$x = array(
array(0,0.2,-0.6,-0.4),
array(-0.2,0,0.4,2),
array(-0.2,0.4,0,0.6)
);
$s = array(
0,0,0
);
echo "0 :: 0 :: 0 :: 0<br>";
for($i=1;$i<100;$i++){
$s[0] = $s[0]*$x[0][0] + $s[1]*$x[0][1] + $s[2]*$x[0][2]+$x[0][3];
$s[1] = $s[0]*$x[1][0] + $s[1]*$x[1][1] + $s[2]*$x[1][2]+$x[1][3];
$s[2] = $s[0]*$x[2][0] + $s[1]*$x[2][1] + $s[2]*$x[2][2]+$x[2][3];
echo $i." :: ".$s[0]." :: ".$s[1]." :: ".$s[2]."<br>";
}
?>

## How to use it ?

just put the X coefficients into the $x array after putting it in the valid form !
## If you have a problem with approximation accuracy use the round() function