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Volume 10, Issue 3
An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

Cuicui Ji & Zhizhong Sun

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 597-613.

Published online: 2017-10

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  • Abstract

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes' first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Grünwald-Letnikovv difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of $\mathcal{O}(τ^2+h^4)$ in maximum norm, where  $τ$ and $h$ are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

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@Article{NMTMA-10-597, author = {Cuicui Ji and Zhizhong Sun}, title = {An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {3}, pages = {597--613}, abstract = {

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes' first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Grünwald-Letnikovv difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of $\mathcal{O}(τ^2+h^4)$ in maximum norm, where  $τ$ and $h$ are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1605}, url = {http://global-sci.org/intro/article_detail/nmtma/12360.html} }
TY - JOUR T1 - An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative AU - Cuicui Ji & Zhizhong Sun JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 597 EP - 613 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1605 UR - https://global-sci.org/intro/article_detail/nmtma/12360.html KW - AB -

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes' first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Grünwald-Letnikovv difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of $\mathcal{O}(τ^2+h^4)$ in maximum norm, where  $τ$ and $h$ are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

Cuicui Ji and Zhizhong Sun. (2017). An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative. Numerical Mathematics: Theory, Methods and Applications. 10 (3). 597-613. doi:10.4208/nmtma.2017.m1605
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