The temperature at some instant (t = 0) of a laterally insulatedsolid rod of 1 unit length is given by ?(?,?) = sin ?? for 0 ? x ?1, where x is measured from left end of the rod to the other end onthe right. Also, at time t = 0, the left end of the rod issubjected to 0oC and maintained over the time, while the right endis insulated when t > 0. Note that the term ?x in the expressionof the temperature is in radian. The temperature variation in therod,
?(?,?), satisfies the heat equation: ?? ?? = ?( 2 ?^2? /??^ 2)
Solve the above heat equation numerically with ?del x = 0.2 and?del t = 0.04 using explicit formula: ?(?? ,??+1) = ??(???1,??) +(1 ? 2?)?(?? ,??) + ??(??+1,??)
Given that, c ^2 = 0.1 and ? = ? ^2 ?? (??)2 .
Estimate the numerical values for ?(?,?) at t = 0.08, givingyour answers at 4 decimal points
