Write a similar Python codsyms h

$A=\left[\begin{array}{ccccccccccccccccccccccc}1& 1& 1& 1& 1\text{;}-2& -1& 0& 1& 2\text{;}4& 1& 0& 1& 4\text{;}& -8& -1& 0& 1& 8\text{;}& 16& 1& 0& 1& 16\end{array}\right]$;

$b={\left[\begin{array}{ccccc}0& 0& \frac{2}{h^{{?}^{{?}^{?}}}}2& 0& 0\end{array}\right]}^{\text{'}}$;

$\%$ solve the linear system of equations to obtain the coeffiecients

$x=\frac{A}{\frac{?}{?}}b$

fdstencil $(2,-2$:$2)$

uptrue $=-4**sin(2)$;

sixth$\_$derivative $=-64**sin(2)$;

hvals $=$ logspace $(-1,-4,13)$;

$D5u=[]$;

$E5u=[]$;

E$5$u$\_$pred $=[]$;

$\%$ table headings

disp $(\text{'}\text{'})$

disp$(\text{'}$ h

D$5$u

E$5$u$\text{'})$

for $i=1$ : length $($hvals$)$

$h=$ hvals$($i$)$;

$xpts=1+h***(-2$:$2{)}^{\text{'}}$;

D$5$u$($i$)=$fdcoeffF$(2,1,xpts)**sin(2**xpts)$;

$$rror

E$5$u$($i$)=$ D$5$u$($i$)-$uptrue;

E$5$u$\_$pred $=-0\mathrm{.}0111111**(h^{{?}^{{?}^{?}}}4)**$ sixth$\_$derivative;

disp $($sprintf $(\text{'}\%13\mathrm{.}8$e

$\%15\mathrm{.}8e$

$15\mathrm{.}8e^{\text{'}},$

h$,$ D$5$u$($i$),$ E$5$u$($i$)))$

end

$$ Plot errors

Clf

loglog $($hvals$,$abs $($E$5$u$),\text{'}-\text{'})$

hold on

loglog$($hvals$,$abs $($E$5$u$\_$pred$),\text{'}-\text{'})$

title$(\text{'}$log log plot of errors vs h$\text{'})$

xlabel $(\text{'}$h$\text{'})$

ylabel$(\text{'}$Errors $($E$5$u$)\text{'})$

legend$(\text{'}$Numerical Error','Predicted Truncation Error','Location', 'North'$)$

hold offe of this matlab code.

clc; clear; close all;

$\%$ Problem $2$

syms h

A $=[11111$;$-2-1012$; $41014$; $-8-1018$; $1610116]$;

b $=[002/$h$^200]\text{'}$;

$\%$ solve the linear system of equations to obtain the coeffiecients

x $=$ A$\backslash$b

fdstencil$(2,-2$:$2)$

uptrue $=-4*$sin$(2)$;

sixth$\_$derivative $=-64*$sin$(2)$;

hvals $=$ logspace$(-1,-4,13)$;

D$5$u $=[]$;

E$5$u $=[]$;

E$5$u$\_$pred $=[]$;

$\%$ table headings

disp$(\text{'}\text{'})$

disp$(\text{'}$ h D$5$u E$5$u$\text{'})$

for i$=1$:length$($hvals$)$

h $=$ hvals$($i$)$;

xpts $=1+$h$*(-2$:$2)\text{'}$;

D$5$u$($i$)=$ fdcoeffF$(2,1,$xpts$)*$sin$(2*$xpts$)$;

$\%$ Error

E$5$u$($i$)=$ D$5$u$($i$)-$uptrue;

E$5$u$\_$pred $=-0\mathrm{.}0111111*($h$^4)*$sixth$\_$derivative;

disp$($sprintf$(\text{'}\%13\mathrm{.}8$e $\%15\mathrm{.}8$e $\%15\mathrm{.}8$e$\text{'},$

h$,$D$5$u$($i$),$E$5$u$($i$)))$

end

$\%$ Plot errors

clf

loglog$($hvals$,$abs$($E$5$u$),\text{'}$o$-\text{'})$

hold on

loglog$($hvals$,$abs$($E$5$u$\_$pred$),\text{'}-\text{'})$

title$(\text{'}$log log plot of errors vs h$\text{'})$

xlabel$(\text{'}$h$\text{'})$

ylabel$(\text{'}$Errors $($E$5$u$)\text{'})$

legend$(\text{'}$Numerical Error','Predicted Truncation Error','Location','North'$)$

hold off