$\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}+U[\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{y}}]=0$

where $U$ is the phase speed and positive and $U=15\frac{m}{s},x$ and $y$ are in units of meter and $t$ in units of

second. The field of $T$ at time $t=0($initial condition$)$ is given by

Write a python program to solve Eq$.(7),$ subject to the initial conditions given in Eq$.(8),$ for $($i$)$ Leap$-$frog scheme in time and centered difference in space, and $($ii$)$ Forward scheme in time and backward scheme in space.