Abstract
The model applies a second-order, two-step, precise numerical scheme for solving time-dependent convection-diffusion in both science and engineering. The proposed scheme combines the classical Euler scheme with a modified exponential time integrator to form an explicit predictor-corrector algorithm. To achieve high spatial resolution, a compact finite-difference scheme is used. The method is applied to a mixed convective magnetohydrodynamic flow model over a stationary vertical sheet, incorporating the effects of an inclined magnetic field and oscillatory thermal and concentration boundary conditions. A detailed stability and convergence analysis is carried out using von Neumann analysis and Taylor series expansion. According to the simulation results, a higher magnetic tilt slows down fluid motion, and a higher Darcy number improves the velocity profile. Oscillatory boundary conditions cause the temperature and concentration fields to stratify periodically. The proposed system demonstrates superior accuracy and computational efficiency compared to conventional Euler and second-order Runge-Kutta algorithms. Results show that the suggested model for complicated transport processes in porous media is both accurate and useful in practice.