Abstract
This contribution proposes a third-order numerical scheme for solving time-dependent partial differential equations (PDEs). This third-order scheme is further modified, and the new scheme is obtained with second-order accuracy in time and is unconditionally stable. The unconditional stability of the new scheme is proved by employing von Neumann stability analysis. For spatial discretization, a compact fourth-order accurate scheme is adopted. Moreover, a mathematical model for heat transfer of Darcy-Forchheimer flow of micropolar fluid is modified with an oscillatory sheet, nonlinear mixed convection, thermal radiation, and viscous dissipation. Later on, the dimensionless model is solved by the proposed second-order scheme. The results show that velocity and angular velocity have dual behaviors by incrementing coupling parameters. The proposed second-order accurate in-time scheme is compared with an existing Crank-Nicolson scheme and backward in-time and central in space (BTCS) scheme. The proposed scheme is shown to have faster convergence than the existing Crank-Nicolson scheme with the same order of accuracy in time and space. Also, the proposed scheme produces better order of convergence than an existing Crank-Nicolson scheme.