Question: Differential equations like the one solved in Prob. 27.6 can often be simplified by linearizing their nonlinear terms. For example, a first-order Taylor series expansion
Differential equations like the one solved in Prob. 27.6 can often be simplified by linearizing their nonlinear terms. For example, a first-order Taylor series expansion can be used to linearize the quartic term in Eq. (P27.6) as
1 x 10-7 (T + 273)4 = 1 x 10-7 (Tb + 273)4 + 4
x 10-7 (Tb + 273)3 (T - Tb)
Where Tb is a base temperature about which the term is linearized. Substitute this relationship into Eq. (P27.6), and then solve the resulting linear equation with the finite-difference approach. Employ Tb= l50 and ∆x = 0.0l to obtain your solution.
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The secondorder ODE can be linearized as in Substituting T b 150 and collecting terms gives ... View full answer
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