On the Properties of Two-Dimensional Normalized Boubaker Polynomials
Mohammed Abdelhadi Sarhan, Suha SHIHAB, Mohammed Rasheed
Abstract
The aim of the present work deals with newly defined two-variable polynomials for normalized Boubaker . The operational matrices of derivatives with respect to the two variables are presented at first with explicit expression. Then, a normalized Boubaker polynomial approximation for the numerical solution of a class of partial differential equations is proposed, depending on a truncated, normalized Boubaker function series in the equation together with the operational matrices in the proposed partial differential equation. The original partial differential equation is reduced under consideration of a system of simply solvable algebraic equations. Due to the interesting derived properties of normalized Boubaker polynomials in two variables, the suggested method can achieve good results with few complexities. Using operational matrices of derivatives, one can save computation and more memory. Two-dimensional examples are listed to show the satisfactory level of the suggested method.