Integration of Difficult Initial and Boundary Value Problems by Arc-Length Strategy

For differential equations exhibiting steep gradients and large curvature of the solution, the arc-length transformation has been proposed. The transformed differential equations can be accurately represented by a small number of equally spaced mesh points. The transformation can be used both for initial and boundary value problems. This transformation proved to be useful for reactor, flame and combustion problems, calculation of dissipative structures and transient behavior of certain autocatalytic reactions. Three sample examples are solved.