Hermite Fitted Block Integrator for Solving Second-Order Anisotropic Elliptic Type PDEs

A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study. The method derived through collocation interpolation techniques using the polynomial as basis function. interpolated at first two successive points, while occurred all suitably chosen points. major scheme its complementary were united together to form HFBI. analysis of HFBI showed that it had a convergence order eight with small error constants, zero-stable, absolutely-stable, satisfied condition convergence. In confirm usefulness, accuracy, efficiency HFBI, lines approach applied discretize equation PDE into system ODEs consequently used obtain approximate solutions PDEs. computed solution generated by compared exact problems other existing methods literature. proposed favorably methods, which validated test whose are presented tabular form, comparisons illustrated curves.