Numerical Simulations of Solving Heat-Conduction PDE (Partial Differential Equation) Using ZT (Zhang-Taylor) Time-Discretization Formula Extended from Neurodynamics

Partial differential equations (PDEs) provide an accurate representation of mathematical and physical relationships in many modern engineering applications. In this paper, we utilize the Zhang-Taylor (ZT) time-discretization formula (extended from Zhang neurodynamics) as an alternative to Euler forward-difference formula. Utilizing the ZT time-discretization formula, the ZT difference algorithm is derived and applied to solve the heat-conduction PDE as an attempt. In addition, the truncation error (TE) of the ZT difference algorithm is derived and verified through numerical simulations. Besides, the numerical simulations including comparative experiments between the Euler difference algorithm and the ZT difference algorithm are conducted. Numerical results show that the ZT difference algorithm (extended from Zhang neurodynamics) is feasible and effective for solving the heat-conduction PDE.