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A Third-Order Two-Stage Numerical Scheme for Fractional Stokes Problems: A Comparative Computational Study


 A third-order explicit-implicit fractional scheme is proposed for solving fractional partial differential equations. The first explicit stage has the advantage of converging fast, and the second step is responsible for enlarging the stability region. The fourth-order compact scheme is employed to discretize spatial derivative terms. The stability of the scheme is given for standard parabolic equation with linear source term, whereas convergence of the proposed scheme is given for parabolic equation with nonlinear source term. A mathematical model of heat and mass transfer of Stoke's first problem using Dufour and Soret effects is given in the form of partial differential equations. Later on, these governing equations are converted to dimensionless forms. The fractional form of the dimensionless model is solved numerically by the proposed schemes, and comparison is also conducted with existing schemes.