Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems.

In the era of computational advancements, harnessing computer algorithms for approximating solutions to differential equations has become indispensable for its unparalleled productivity. The numerical approximation of partial differential equation (PDE) models holds crucial significance in modelling physical systems, driving the necessity for robust methodologies. In this article, we introduce the Implicit Six-Point Block Scheme (ISBS), employing a collocation approach for second-order numerical approximations of ordinary differential equations (ODEs) derived from one or two-dimensional physical systems.