Question:what is the error of second order of pde

Question:what is the error of second order of pde

Maple

restart:

sys:={-diff(v(x,t),t)+0.5*p*diff(u(x,t),x,x)+q*u(x,t)*(u(x,t)^2+v(x,t)^2)=0,diff(u(x,t),t)+0.5*p*diff(v(x,t),x,x)+q*v(x,t)*(u(x,t)^2+v(x,t)^2)=0};
/                      /  2         \
|/ d         \         | d          |
sys := < |--- u(x, t)| + 0.5 p |---- v(x, t)|
|\ dt        /         |   2        |
\                      \ dx         /

/       2          2\       / d         \
+ q v(x, t) \u(x, t)  + v(x, t) / = 0, -|--- v(x, t)|
\ dt        /

/  2         \                                      \
| d          |             /       2          2\    |
+ 0.5 p |---- u(x, t)| + q u(x, t) \u(x, t)  + v(x, t) / = 0 >
|   2        |                                      |
\ dx         /                                      /
eq1 := diff(u(x,t),t) = u__t(x,t):
eq2 := diff(v(x,t),t) = v__t(x,t):

sys_tmp := subs(eq1, eq2, sys):

sys_new := sys_tmp union {eq1, eq2}:

Boundary conditions:
bc :=
u(0,t) = 2,
v(0,t) = 0;
bc := u(0, t) = 2, v(0, t) = 0
Initial conditions:
ic :=
u(x,0) = tanh(2*Pi),
v(x,0) = tanh(2*Pi),
u__t(x,0) = 0,
v__t(x,0) = 0;

ic := u(x, 0) = tanh(2 Pi), v(x, 0) = tanh(2 Pi), u__t(x, 0) = 0,

v__t(x, 0) = 0
Solve the system:
pdsol := pdsolve(subs(p=1, q=0.5, sys_new), {ic, bc}, numeric);

﻿