. The object-ive 01 t.his research is t.o minimize t.he error andcomput.at.ional t.ime 01 t.he Boundary Element. Met.hod (BEM)In t.he f’i r-s t. part- 01 t.he research, a det.ailed descript.ion 01the BEM is given, start.ing f r-orn t.he analyt-ical derivat-ion 01 t.heboundary int-egral equat.ion t-o t-he capabili t.ies of t.his met.hod int-he descript-ion of complex geomet-ries and mult-i layered domainsIn t-he second p a r-t., a review 01 t.he work done using t-he BEM,is given. This work ranges f r-orn a minimizat.ion 01 error in t-heBEM,po t.e rrt.i ed,heat.dillusion,t-oitsapplicat-iont.owavepropagation, elect.rical and mechanical problems .In t.he third part. 01 t.he work, t.wo modiIications t.o t.he BEl-!are proposed; in order t.o reduce t.he error1- A variation in Le g e rrdr-e polynomial order using a scalingparamet-er Nr2- The use 01 separat.ed boundary element-s for t.he descript.ion01 systems with mixed boundary condit-ionsFinally, in the lourth p ar-t., the potential dist.ribut.ion int.he deplet.ion region PN t.ype semiconduct.ors is obt.ained using t.heboundary solut.ion and t.he BEM .The domain Irrt.e r-g r-ed result.s in t.heBEM lormulat.ion isreduced analyt.ically to a line int.egral. The proposed method hast.he advant.age 01 reducing1- The dimensions 01 t.he problem2- The comput.at.ional t.ime .