TY - EJOU
AU - Chang, Chih-Wen
AU - Chang, Jiang-Ren
AU - Liu, Chein-Shan
TI - The Lie-Group Shooting Method for Solving Classical Blasius Flat-Plate Problem
T2 - Computers, Materials \& Continua
PY - 2008
VL - 7
IS - 3
SN - 1546-2226
AB - In this paper, we propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf **G**(*T*) and the formation of a generalized mid-point Lie group element$\mathbf **G**(*r*). Then, by imposing **G**(*T*) = **G**(*r*) we can derive some algebraic equations to recover the missing initial conditions. It is the first time that we can apply the Lie-group shooting method to solve the classical Blasius flat-plate problem. Numerical examples are worked out to persuade that the novel approach has better efficiency and accuracy with a fast convergence speed by searching a suitable r ∈(0, 1) with the minimum norm to fit the targets.
KW - One-step group preserving scheme
KW - Blasius equation
KW - Boundary value problem
KW - Shooting method
KW - Estimation of missing initial condition
DO - 10.3970/cmc.2008.007.139