Computational approaches for singularly perturbed turning point problems with non-local boundary conditions

Abstract

In this research article, a computational method is introduced to address the turning point problem (TPP) of second-order differential equation with integral boundary condition (IBC). Due to the presence of turning point at $s=0$, the problem exhibit boundary layer at $s=-1$ and $s=1$. The discretization process for these differential equations employs the finite difference scheme, while the integration conditions are discretized using the Trapezoidal rule, applied on piecewise uniform meshes known as Shiskin mesh. The proposed method is close to first order convergent. Some numerical examples are provided to validate the theoretical results.