One-step fourth derivative block integrator for the numerical solution of singularly perturbed third-order boundary value problems

Abstract

Third-order singularly perturbed problems are common models that are prevalent in applied mathematics and engineering. They model physical phenomenon in fluid dynamics, optimal control, reaction-diffusion processes, and many other fields. A one-step fourth derivative block integrator is derived in this work to numerically solve general singularly perturbed third-order problems in ordinary differential equations with prescribed initial or boundary conditions. The derivation of this block of integrators was achieved via the collocation technique where a shifted Chebyshev polynomial of the first kind is used as the trial solution. The characteristics of the method are shown and the numerical examples shows an excellent performance in terms of accuracy of this block method as compared to existing methods already in literature.