Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

Figure 1

Approximations for the expectation E[𝑢(𝑥,𝑡)] (a), and the standard deviation Var[𝑢(𝑥,𝑡)] (b), on the spatial domain 0≤𝑥≤50 for some selected values in the time interval 0<𝑡≤100 in the context of Example 1.

(a)

(b)