Non-linear relaxation methods: I. An operator formalism

✍ Scribed by S.K. Rangarajan

• Publisher: Elsevier Science
• Year: 1974
• Weight: 973 KB
• Volume: 56
• Category: Article
• ISSN: 0022-0728
• DOI: 10.1016/s0022-0728(74)80314-1

✦ Synopsis

f (r), g(~), gtkr) gii, ,9o'iJ g,g area of the electrode jth order term in the expansion czf/7 r~(j , I~ v,(j, Lk } t z*lm I Nlmk * •nthegenera•casef(E)andgk(E)themse•vesmaybeexpandedasfuncti•na•sratherthanas(uncti•ns of 6E. But for our applications, such an extension seems unnecessary.

** Note the definition of the g~r) and gOtr); {g~r)} are of the order (6E)' whereas got,), the coefficients, are of the order unity, * One may wonder "where?" since nowhere in eqns. ( )-( ) hE is explicitly present. But fE is very much there through terms like g~2~, f~2).., oc (rE) 2 and A ~2), GC2)... etc. Thus one has fiE-dependence through G~r), A~r), f~r~ etc.; r= 1, 2, 3,... * Similar results are available with the author for the perturbation terms in 6E given the current 3if. ** viz. evaluating the operation of )~ on a given function or equivalently knowing K.