Matlab question in French. Please check my code and helo with the Picture with the question. i am not able to make it work

$\%$ Function definitions

P $=$ @$($x$)-1./$ x; $\%$ Definition of p$($x$)$

Q $=$ @$($x$)0*$ x; $\%$ Definition of q$($x$)$

R $=$ @$($x$)-1\mathrm{.}6./($x$.^4)$; $\%$ Definition of r$($x$)$

a $=0\mathrm{.}9$; b $=1$; alpha $=0$; beta $=1$;

$\%$ Parameters

h$1=0\mathrm{.}01$;

h$2=0\mathrm{.}005$;

N$1=$ round$(($b $-$ a$)/$ h$1-1)$;

N$2=$ round$(($b $-$ a$)/$ h$2-1)$;

x$1=$ linspace$($a $+$ h$1,$ b $-$ h$1,$ N$1)$;

x$2=$ linspace$($a $+$ h$2,$ b $-$ h$2,$ N$2)$;

P$1=$ P$($x$1)$;

Q$1=$ Q$($x$1)$;

R$1=$ R$($x$1)$;

P$2=$ P$($x$2)$;

Q$2=$ Q$($x$2)$;

R$2=$ R$($x$2)$;

$\%$ V$$rification des tailles

disp$(\text{'}$Tailles de P$1,$ Q$1,$ R$1$ :$\text{'})$;

disp$($size$($P$1))$;

disp$($size$($Q$1))$;

disp$($size$($R$1))$;

disp$(\text{'}$Tailles de P$2,$ Q$2,$ R$2$ :$\text{'})$;

disp$($size$($P$2))$;

disp$($size$($Q$2))$;

disp$($size$($R$2))$;

$\%$ Compute solutions

y$1=$ problimite$($N$1,$ P$1,$ Q$1,$ R$1,$ a$,$ b$,$ alpha, beta$)$;

y$2=$ problimite$($N$2,$ P$2,$ Q$2,$ R$2,$ a$,$ b$,$ alpha, beta$)$;

$\%$ Exact solution

c $=1\mathrm{.}4$; d $=0\mathrm{.}81$;

x$\_$exact $=$ linspace$($a$,$ b$,50)$;

y$\_$exact $=($c $-0\mathrm{.}4./$ x$\_$exact.$^2)-($c $-0\mathrm{.}4/$ d$)*($log$($x$\_$exact$)/$ log$(0\mathrm{.}9))$;

$\%$ Plot

plot$($x$\_$exact, y$\_$exact, $\text{'}--\text{'},$ 'LineWidth', $2)$;

hold on;

plot$($x$1,$ y$1,$ 'LineWidth', $2)$;

plot$($x$2,$ y$2,$ 'LineWidth', $2)$;

legend$(\text{'}$Exact solution', $\text{'}$h $=0\mathrm{.}01\text{'},\text{'}$h $=0\mathrm{.}005\text{'})$;

xlabel$(\text{'}$x$\text{'})$;

ylabel$(\text{'}$y$\text{'})$;

title$(\text{'}$Approximations num$$riques vs Solution exacte'$)$;

grid on;

hold off;

$\%$ Calculation of error

Nbr$\_$pt $=600$;

Erreur$\_$h $=$ zeros$(1,$ Nbr$\_$pt$)$;

for ii $=1$:Nbr$\_$pt

N $=$ ii;

h$\_$i $=($b $-$ a$)/($ii $+1)$;

h$\_$valeurs$($ii$)=$ h$\_$i;

x$\_$i $=$ linspace$($a $+$ h$\_$i$,$ b $-$ h$\_$i$,$ N$)$;

x$\_$i$\_$inter $=$ x$\_$i$(2$:end $-1)$;

P$\_$err $=$ P$($x$\_$i$\_$inter$)$;

Q$\_$err $=$ Q$($x$\_$i$\_$inter$)$;

R$\_$err $=$ R$($x$\_$i$\_$inter$)$;

y$\_$boucle $=$ problimite$($N$,$ P$\_$err, Q$\_$err, R$\_$err, a$,$ b$,$ alpha, beta$)$;

y$\_$boucle $=$ y$\_$boucle';

y$\_$exacte$\_$i $=(1\mathrm{.}4-0\mathrm{.}4./$ x$\_$i$\_$inter.$^2)-(1\mathrm{.}4-0\mathrm{.}4/0\mathrm{.}81)*($log$($x$\_$i$\_$inter$)/$ log$(0\mathrm{.}9))$;

erreur $=$ abs$($y$\_$boucle $-$ y$\_$exacte$\_$i$)$;

Erreur$\_$h$($ii$)=$ max$($erreur$)$;

end

$\%$ Plot of the error

figure;

loglog$($h$\_$valeurs, Erreur$\_$h$,$ 'LineWidth', $2)$;

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

ylabel$(\text{'}$Erreur$\text{'})$;

title$(\text{'}$Erreur en fonction de la taille du pas $($h$)\text{'})$;

grid on;

function x $=$ tridiagonal$($D$,$ L$,$ U$,$ B$)$

$\%$ Get the length of the main diagonal

n $=$ length$($D$)$;

$\%$ Construct the sparse tridiagonal matrix A

A $=$ spdiags$([$L D U$],-1$:$1,$ n$,$ n$)$;

$\%$ Solve the system Ax $=$ B

tic; $\%$ Start timer

x $=$ A $\backslash$ B;

toc; $\%$ End timer and display elapsed time

end

function y $=$ problimite$($N$,$ P$,$ Q$,$ R$,$ a$,$ b$,$ alpha, beta$)$

$\%$ Initialize vectors for the tridiagonal system

D $=$ zeros$($N$,1)$;

L $=$ zeros$($N $-1,1)$;

U $=$ zeros$($N $-1,1)$;

B $=$ zeros$($N$,1)$;

$\%$ Fill the vectors based on P$,$ Q$,$ R$,$ and other parameters

for i $=1$:N

D$($i$)=$ P$($i$)+$ Q$($i$)+$ R$($i$)$;

B$($i$)=$ a $*$ i$^2+$ b $*$ i;

if i $>1$

L$($i $-1)=$ P$($i$)-$ Q$($i $-1)$;

end

if i $$ N

U$($i$)=$ P$($i$)-$ Q$($i$)$;

end

end

$\%$ Solve the tridiagonal system

y$\_$interior $=$ tridiagonal$($D$,$ L$,$ U$,$ B$)$;

$\%$ Construct the complete solution vector

y $=[$alpha; y$\_$interior; beta$]$;

end

it shows lik that :

Classroom License $--$ for classroom instructional use only.

$>>$ aaaaa

Tailles de P$1,$ Q$1,$ R$1$ :

$19$

$19$

$19$

Tailles de P$2,$ Q$2,$ R$2$ :

$119$

$119$

$119$

Error using horzcat

Dimensions of arrays being concatenated are not consistent.

Error in aaaaa$>$tridiagonal $($line $96)$

A $=$ spdiags$([$L D U$],-1$:$1,$ n$,$ n$)$;

Error in aaaaa$>$problimite $($line $124)$

y$\_$interior $=$ tridiagonal$($D$,$ L$,$ U$,$ B$)$;

Error in aaaaa $($line $40)$

y$1=$ problimite$($N$1,$ P$1,$ Q$1,$ R$1,$ a$,$ b$,$ alpha, beta$)$;

$>>$