Abstract:
Very few nonlinear probkms can be solved exactly but it is sometimes possible to
expand solution in powers of some parameters. In practice the presence of singularities
pre~ents rapid convergence of lhe series, so it lS necessary to seck an efficient
approximate method. Our purpose is to analyze the dominating singularity behavior of a
few problems and the performance of approximate methods.
The aim of this thesis is to analyze the approxImate methods by applying them to various
model problems, Firstly, we have applied them to some standard problems, whose
singularities are known. Secondly we have analyzed numerically the critical behavior of
the solutions 0r two non-linear ditTercntiaiequations.
Finally, we have studied the fklwina porous pipe with dcce1eratmgwall for analy~ingthe
dominant singularity behavior of the flow. The series related to the Reynolds number R
is developed by using algebraic programming language MAPLE, The series i, then
analyzed by variou, generalizations of the approximate methods. We observe that the
convergence or both the series 1S limited by the dominating singularity located at
R = R, '" 3,0724980042 and surprisingly there IS another turning point at
R, '" 8.813114939 .The result concluded that there is a reversal now at the walL
