Generalized Lucas Tau Method for the Numerical Treatment of the One and Two-Dimensional Partial Differential Heat Equation

This paper is dedicated to proposing two numerical algorithms for solving the one- and two-dimensional heat partial differential equations ( PDEs ). In these algorithms, generalized Lucas polynomials id="M2"> GLPs ) involving parameters are utilized as basis functions. The proposed schemes in one two- dimensions based on corresponding integral equation equation, after that employing, respectively, tau collocation methods convert subject their underlying conditions into systems of linear algebraic can be treated efficiently via suitable procedures. this article, convergence analysis examined expansion. Five illustrative problems numerically solved show applicability accuracy presented algorithms. Our obtained results compare favourably with exact solutions.