Computational Physics, Physics, Heat Equation, Python, Math.
at L, so 0 and L are the boundaries of X, where L is the length of a rod. To solve such equations, an initial condition is needed, e.g 𝑢(𝑥,0) = 𝑢₀(𝑥), meaning that the temperature at the time 0 is 𝑢₀(𝑥). The initial condition is always some function, which represent the temperature of all points at