Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

作者：Chen Chang Ming; Liu F^*; Burrage K; Chen Y

来源：IMA Journal of Applied Mathematics, 2013, 78(5): 924-944.

DOI：10.1093/imamat/hxr079

• variable-order fractional derivative
• Rayleigh-Stokes problem
• implicit numerical method
• explicit numerical method
• convergence
• stability
• solvability
• Fourier analysis

Rayleigh-Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

• 出版日期2013-10
• 单位厦门大学