Abstract:
The modellmg of physical phenomena usually results to nonlinear problems whose
solutions may have singularities Practically tile locations of tile singularities are
important for many problem" a solution can be Iuwld as a series in powers of one or
~everal independent variable" In this thesis under the title "A New Approach To Partial
Differential ApprOXllnanto" we ha,e analysed series L11p<Jwer~ of lwo independent
variable; hy HLgh-ordeLpartial differelltl1l1approxlInanls We have developed the method
using the concepl or I'mk-Hel"lllJle c1a%, II consists of a high-order linear partial
differenlial equation with polynomi~1 eoen"Lciems that is satlsfied appruxlmalely by the
partial sum of the muhivariable po\\'er serie.1
We have also reviewed the different approximant methods lor the summation or series in
powers of one or more Independent variables Our aml I, to apply the new method to
problems in phy~icailield, patlicularly in fluid dynamics.
