Symmetry reduction and numerical solution of a third-order ODE from thin film flow

Abstract

A new approach to solving high-order ordinary differential equations numerically is presented. Instead of the usual approach of writing a high-order ordinary differential equation as a system of first-order ordinary differential equations, we write the high-order ordinary differential equation in terms of its differential invariants. The third-order ordinary differential equation y′′′ = y−k for constant k is used to illustrate this approach for the cases k = 2 and k = 3.