Numerical Convergence Analysis of the Frank-Kamenetskii Equation.

This work investigates the convergence dynamics of a numerical scheme employed for the approximation and solution of the Frank-Kamenetskii partial differential equation. A framework for computing the critical Frank-Kamenetskii parameter to arbitrary accuracy is presented and used in the subsequent numerical simulations. The numerical method employed is a Crank-Nicolson type implicit scheme coupled with a fourth order spatial discretisation as well as a Newton-Raphson update step which allows for the nonlinear source term to be treated implicitly.