Matrix Exponentiation and the Frank-Kamenetskii Equation

Figure 2

Plot comparing the log|𝑢^𝑗_𝑖−𝑦^∗_𝑖| for 𝑗=10,100, and 1000, respectively, where we have chosen 𝛿=1, Δ𝑥=0.005, Δ𝑡=0.00001, and 𝑘=1. We have used (3.18) as the initial value of the numerical schemes where LE scheme corresponds to the Lawson-Euler scheme (3.8), BDF scheme corresponds to the numerical scheme (3.11), and RK4 scheme corresponds to the numerical scheme (3.12).

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