scholarly journals A fractional step method for 2D parabolic convection-diffusion singularly perturbed problems: uniform convergence and order reduction

2016 ◽  
Vol 75 (3) ◽  
pp. 809-826 ◽  
Author(s):  
C. Clavero ◽  
J. C. Jorge
Keyword(s):  
Uniform Convergence ◽  
Order Reduction ◽  
Singularly Perturbed ◽  
Fractional Step ◽  
Singularly Perturbed Problems ◽  
Step Method ◽  
Fractional Step Method ◽  
Convection Diffusion

scholarly journals Comparison of Efficient Explicit Schemes for Shallow-Water Equations—Characteristics-Based Fractional-Step Method and Multimoment Eulerian Scheme

2007 ◽  
Vol 46 (3) ◽  
pp. 388-395 ◽  
Author(s):  
Yohsuke Imai ◽  
Takayuki Aoki ◽  
Magdi Shoucri
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Parallel Architecture ◽  
Fractional Step ◽  
Processing Unit ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Processing ◽  
Explicit Schemes ◽  
Coarse Meshes

Abstract Two explicit schemes for the numerical solution of the shallow-water equations are examined. The directional-splitting fractional-step method permits relatively large time steps without an iterative process by using a treatment based on the characteristics of the governing equations. The interpolated differential operator (IDO) scheme has fourth-order accuracy in time and space by using a Hermite interpolation function covering local domains, and accurate results are obtained with coarse meshes. It is shown that the two schemes are very efficient for hydrostatic meteorological models from the viewpoints of numerical accuracy and central processing unit time, and the fact that they are explicit makes them suitable for computers with parallel architecture.

The fully discrete fractional-step method for the Oldroyd model

2018 ◽  
Vol 129 ◽  
pp. 83-103 ◽  
Author(s):  
Tong Zhang ◽  
Yanxia Qian ◽  
JinYun Yuan
Keyword(s):  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Oldroyd Model ◽  
Fully Discrete
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