Singular Perturbation Approximation Research Articles

On Poincar�'s second species solutions

A proof of the existence of Poincare's second species solution in the restricted three body problem is given. It is not based, as Perko's and Guillaume's work, on singular perturbation and asymptotic approximation but rather on topological equivalence between differential systems in the neighborhood of an equilibrium.

Singular perturbation for nonlinear boundary‐value problems

Asymptotic solutions of a class of nonlinear boundary‐value problems are studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular‐perturbation type and approximations are constructed by the method of matched asymptotic expansions.

Dispersion calculations in nonuniform seepage

A singular perturbation approximation is derived and applied to some examples in groundwater dispersion. This approximation is general enough to be used for nonuniform, steady and unsteady seepage through heterogeneous aquifers, and it complements numerical methods since it becomes most accurate in regions where accurate numerical solutions are almost impossible to obtain.