SPICE OF SOLUTIONS TO SINGULARLY PERTURBED EQUATIONS

Abstract

The subject of the research is the singularly perturbed differential equation of Lighthill, the aim of the research is the splicing of solutions of the model Lighthill equation. The splicing method consists of two methods: the classical method and the parameterization method. The splicing process itself consists of three stages: finding an external solution, building an internal solution, and splicing solutions. This method was first introduced by L. Prandtl. This method is used for equations with a small parameter at the highest derivative. Far from the boundary, the solution changes slowly, where formally small terms can be discarded, since the equation is of reduced order. At the border, the decision, unlike the internal one, changes quickly. This also means external decomposition. The senior derivatives are also important here. You need to know that external and internal solutions are one and the same solution in different forms.