An \(\varrho \)-uniformly convergent technique for singularly perturbed problems, with an interior turning point occurring in chemical processes

A parameter-uniform solution is presented for singularly perturbed turning point problems with twin boundary layers. A fitted mesh is created in order to resolve the layers, and the provided equation is discretized using the cubic B-spline basis functions on this mesh. For the analytic solution and its derivatives, asymptotic bounds are provided. A brief analysis shows that the method is first-order precise in time and second-order accurate (up to a logarithm factor) in space, and that it is uniformly convergent regardless of the minuscule parameter. Two test problems are offered in order to verify the theoretical results.