The Lax$-$Wendroscheme is dened by

Un$+1$

j $=$

$1$

$2$

$(1+)$ Un

j$1+(12)$ Un

j $$

$1$

$2$

$(1)$ Un

j$+1$:

check that

jR $()$j$2=142$

$12$

sin$4$ x

$2$

:

Deduce that the Lax$-$Wendro scheme is stable when jj $1$:

Implement the Lax$-$Wendro scheme in Matlab.