Abstract
The well-known Stokes' problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes' problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes' problems of finite and infinite depths.
| Original language | English |
|---|---|
| Article number | 5693276 |
| Journal | Mathematical Problems in Engineering |
| Volume | 2018 |
| DOIs | |
| Publication status | Published - 2018 Jan 1 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Engineering(all)
Cite this
}
Application of Adomian Decomposition Method to Bounded and Unbounded Stokes' Problems. / Liu, Chi Min; Yang, Ray-Yeng.
In: Mathematical Problems in Engineering, Vol. 2018, 5693276, 01.01.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - Application of Adomian Decomposition Method to Bounded and Unbounded Stokes' Problems
AU - Liu, Chi Min
AU - Yang, Ray-Yeng
PY - 2018/1/1
Y1 - 2018/1/1
N2 - The well-known Stokes' problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes' problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes' problems of finite and infinite depths.
AB - The well-known Stokes' problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes' problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes' problems of finite and infinite depths.
UR - http://www.scopus.com/inward/record.url?scp=85058811275&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85058811275&partnerID=8YFLogxK
U2 - 10.1155/2018/5693276
DO - 10.1155/2018/5693276
M3 - Article
VL - 2018
JO - Mathematical Problems in Engineering
JF - Mathematical Problems in Engineering
SN - 1024-123X
M1 - 5693276
ER -