Results in Control and Optimization (Sep 2023)
Numerical solution of Advection–Diffusion Equation using Graph theoretic polynomial collocation method
Abstract
Water is one of the main constituents on earth for a living. The Advection Diffusion Equation (ADE) serves as an essential water standard model in environmental engineering since water pollution seriously threatens all life. Hence, the study of ADE has become an increasing concern for researchers in recent years. In the present work, we propose a new numerical method named the Hosoya polynomial collocation method (HPCM) for solving one-dimensional linear ADE. In this work, we developed an operational matrix of Integration of the ortho-normal Hosoya polynomials of path graphs (OHPG) to compute the solute concentration numerically by converting ADE into an algebraic system of equations and solving this system of equations using Newton’s method. With the appropriate collocation approach, we developed a graph theoretic polynomial-based solution to the considered ADE. We presented the convergence analysis, comparisons of HPCM findings with ADE’s analytical solutions, comparisons of error norms, and graphical representations of the numerical conclusions to illustrate the productivity of the HPCM. Comparing numerical results with the outcomes of other current numerical methods ensures the validity of the suggested method’s accuracy and efficacy.
