Innovative numerical method for solving heat conduction using subdivision collocation

Abstract This study introduces a Subdivision Collocation Algorithm (SCA) to numerically solve the Heat Conduction Equation (HCEq), taking into account both initial and boundary conditions. The algorithm reformulates the differential equation into a system of algebraic equations by using subdivision scheme basis functions to approximate spatial derivatives, while finite difference techniques are applied to discretize the time derivatives. The numerical solution of this system is then obtained through computational methods. The effectiveness of the algorithm is confirmed through both theoretical analysis and numerical testing. Additionally, the obtained solutions are presented both numerically and graphically, and compared with existing methods, showing that the proposed algorithm provides higher accuracy than conventional approaches.