The equation should be
v ˙ ( 1 , t ) = ( u ( 2 , t ) − 2 u ( 1 , t ) + u ( 0 , t ) ) ( α Δ x ) 2 {\displaystyle {\dot {v}}(1,t)=\left(u(2,t)-2u(1,t)+u(0,t)\right)\left({\frac {\alpha }{\Delta x}}\right)^{2}}
Return to errata.