Parameter‐uniform numerical methods for some singularly perturbed nonlinear initial value problems

Parameter‐uniform numerical methods for singularly perturbed nonlinear scalar initial value problems are both constructed and analysed in this paper. The conditions on the initial condition for a stable initial layer to form are identified. The character of a stable initial layer in the vicinity of a double root of the reduced algebraic problem is different to the standard layer structures appearing in the neighbourhood of a single stable root of the reduced problem. Results for a problem where two reduced solutions intersect are also discussed. Numerical results are presented to illustrate the theoretical results obtained.