Newton-type iteration around stationary flame equations

Newton-type iteration around stationary flame equations 

The first approach starts from the stationary flame equations in Eulerian coordinates. In their second-order form these equations are obtained by omitting the time derivative from the equations of type (4.19) (cf. Lagrangian representations where the distance derivative on the left-hand side is omitted). The further development, as illustrated by Wilde (1972), is essentially the same 

The linearization as applied to Ri in Eq. (4.39) may also be applied to the right-hand sides of the first-order form of the stationary flame equations, and can again lead to a solution by similar finite-difference techniques (Wilde, 1972). The initial first-order differential equations are obtained by the insertion of appropriate expressions for the and and for Qj and into Eqs. (2.11), (2.12), and (2.21) or (2.22). Convergence is rapid, but again close initial estimates are required. 

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