Study of dominating singularity behavior of series using computer based approximation techniques

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