A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation

A Fast Third-Step Second-Order Explicit Numerical Approach To Investigating and Forecasting The Dynamic of Corruption And Poverty In Cameroon

“…It is worth mentioning that a three-step numerical method is widely encountered in the literature in the form given by formulation (37)- (38). Furthermore, the first characteristic polynomial in term of λ 1 3 of the proposed three-step explicit numerical scheme is defined as…”

“…For such classes of problems, several authors have analyzed a broad range of statistical and numerical methods in approximate solutions. For more details, the readers can consult the works discussed in [25,41,33,55,35,26,38,48,34,43,37,4,29] and references therein. In this paper, we develop an efficient third-step second-order convergent explicit numerical approach for solving a system of nonlinear ODEs modeled by the dynamic of poverty and corruption.…”

Unconditional Stability Of A Two-Step Fourth-Order Modified Explicit Euler/Crank-Nicolson Approach For Solving Time-Variable Fractional Mobile-Immobile Advection-Dispersion Equation

“…The author [21] developed a twostep numerical scheme with convergence order O(τ 2− γ 2 + h 4 ) for solving the time-fractional convectiondiffusion-reaction equation with constant order derivative. For classical integer order ordinary/partial differential equations such as: Navier-Stokes equations, systems of ODEs, mixed Stokes-Darcy model, Shallow water problem, convection-diffusion-reaction equation, advection-diffusion model and conduction equation [18,5,20,24,39,26,29,37,28,27,14,32,23,50], a wide set of numerical techniques have been developed and deeply analyzed. For more details, we refer the readers to [30,38,19,45,33,34,44,22] and references therein.…”

“…Estimate ( 88) is satisfied for any 0 < α < 2 −1 . For n ≥ 1, it comes from ( 15)-( 16) and ( 23)- (24), that…”

A three‐level time‐split MacCormack method for two‐dimensional nonlinear reaction‐diffusion equations

“…Specifically, the hybrid version of MacCormack has been used to solve the mixed Stokes-Darcy and twodimensional time-dependent incompressible Navier-Stokes equations while the three-level time-split Mac-Cormack was applied to two-dimensional time-dependent reaction-diffusion, heat conduction, convectiondiffusion equations and linear/nonlinear convection-diffusion-reaction equations with constant coefficients (diffusive term equals 1 and convective velocity in the range: −1, 0.8 and 1). The analysis has suggested that the three-level explicit time-split MacCormack is fast, second order convergent in time and fourth order accurate in space [26,25,27,24,29,28,23,30,31,32]. We recall that the three-level time-split applies to a time dependent problem of the form: u t = A 1 (u) + A 2 (u), where A j (j = 1, 2) are differential operators, so that each subproblem u t = A j (u), j = 1, 2, is solved independently using the original MacCormack approach.…”