,*_/.,

1. ,*_/., cza--/r.../i -- *%6 - ' \- Proceedings of the 17th rranian conference of ilionredical Dngineerinq (lCtil-JIrl2tl1(l)'3 'l November 2010 of, solutiein A new approaah numericatr f,or valuepl*blerns boundaty singulan nonlinear arising physiolo.gy in Eiham Frasrrenizaden : Kl'csiovv Malcl :;'eiarl School of Mathematics, Iran Universitv of Department of Matherlra.tics Karyj Branch, S (ji{ ) r r c e anCTe: hr . . r l13. r , lt l;ttt'; A zt'rJ. i\/(:ls]1Y ic: Ur Tchran 16846,Iran, K"araj,Iran, ir hashemizadehi@rr; il iau.ac. ad@iust.ac. maleknej andm = 2, a = 0 in the studv of oxygen dilfusion problemin Abstract- In this work a classof nonlinearsingularordinary that arisesin the study ofvarious t:rmor Kinetic>,see[7]-[9]. A differentialequations, cell witf N{ichaelis-\4enten a spherical st:tt:oxl'l{,nrli,'lusion s;heriral :trll r sirnilarprc,b1e..: ;c rritt'I'l = ? r'ni r' = r.l in modellingof growthproblems, stetudy a-i of and the distribution uptakekinetics with Michaelis-Menten heatconductiotr humanhead,see([f 0]-[13]). with /(x,y) in h e a t s o u r c e si n t h r ; b ttm a n Ite r ltl, su lt' cch :' ' ll iln r r n e thodbased is ofthe form o n s h i f t e d L e g en d r e lr o lr ' n r r r ,lisll;. ,^ ,r l tio l a i r r tl 'r i c,;" of a C derivatives for this function are presenlctl to ruuuce tlle : i e '" J , r t > C , , t > 0 . f ( y ) '- (5) f(r,y)= n o n l i n e a r s i n g u la r b o u n d a r y va lu e p r o b le m s th a t ari s,e i n physiology to a system of nonlinear aigebrric :ct'aticrs. fhe resultsfor sr;ch prr;blerns have been Ilxistence-,rniqucrsls method is computationally very simple and itlreltr''e, a.td Il4l-[161. in recentyears, established saveralresearchcis applications are demonstrated through iilustrative exarriplcs" b1' dil;ersi'iialcqualions, solutlo;l::,f r:r'g"'i,r; finding nurncrica, Keywords- !\lotrlinettr ord!t:ttf it(u:,ttaty vL'ltt1 il"t'ittttl; fr{lusof tr.,tsta isitrglrl pi-r'r'i,..;-r1", .-r"irr'.i(r lte'' particularlv 'l) t h t' tf,"rnlic'r :i , r,'rI '.i ' Legendre poll'ootrOr;t i ' a riurnb,er l;'.ir::,.- .'rn::i:.,r,t,;.1r. :3- iJ!I'!,1alf tl'ierrl ci Collocatio n nv! h't d; F )i1s i t r'. gt t in [7]-[20]. q- 'fhe purpose this paperis t/\ rntr)d11.. novel nrethod ol Ilr T Po r - lttC- ' ^ "1 T' based on operati..t'talmat iur-s o. ce'iia,i;'cs of shifled 'fhe aim of this paliei ir',la, i1i',lod.r,l., lrew )rret!1uLi il'Ie iur d pc'11,'n,rnrials lra,t: b.eil !rircdrtcld recentlyin ;hai Legandre numerical solution of rne iollor.r'inr cla.sr oi slngular bountlaty arld rJ:i-gltai,w,:'ik; i2li .'.rl the numerical Saadatmandi value problems scilrltl-tltriri l'r:lntllij' lalue soiuticnil'!|:. :r!.: r,f :illg,'la.t' p r c o l e n r s i 'v r . nr . r - r , : ) ; 1 1 ) , l : r t a r l s ei n ; t 1 ) i i c l r g ) '. I n th i s ( g . y y"(x)+ (", 11) - l'(x,y,,rr r :- 1, '< ';rorlcby lse uf sl'.!l';, I eg:r'irt pcly:::tt:..ii as l:ilil and i-,) i l i i gr r ' !,:,i J i l l /c r ! L -i e s e - '; ' ,,per ati or r al tl t;t1 ,c c ; l ,i .1r l l ,.,r r i of ,.i - .,i .- .,: :]u i - r - r l ti age: :,[:::- 'l ],- o1- 0Qt- ti r !i - .- :: !- i :i n[ r,-r'f0-)-f lltY'(').', '.'., ' ',7') rretf,cd lbr these cliitcLl oil;er io meth:c,L analogy rhis we II ::t.'1'r-ler:tatill, problemsl; , its tr -:.t:y,rt''- :'r';'l e 2.,,i'.1) i),1' (.)'). . i 1, .\. !:; :O pfo\'3 lhiS v r 'I- l r !i LI- :: i ;.Y- i 5r L: ,tl :::l 't oU l i e:ui r l c oni par ed cl ai m. which arising ii' plr;r,;iolo5-i',r'l i,i .lilc .:;,'r f (-i s'. 's . i :1.;.'-:,r-rrcl l ol l o',vs; .:. S ecti ott 2, t' v e a: Thi s pape,,i continuous, .ri exists and is ccnlirr,oL r-t' ;!li{l l i nucduceti si r ;::r l r,g;rl dl ; r'-oi l,l ,.' 'i ai :, :;. i i l :l i l ;r I v v e nl cttti otred sr.i ,r l ri Jtj ettl J.; i rl :,trfr:j r:gt: ..1t; p:i ;rrcttii al s , lt r , : boun, lar vv alue pr obie m ( l ) - 1 3 ) 9 It0,v* 0<x<1. -'" - speci al l y thi i .rp;i ;;rr,,-' i ;,;r.;l i j r'i .'1'j -rl ,'11..,-, .r;,'j i l , .'et i c l d y- l with m = 0,1,,2 cL"';;io':, -*',.;r anda,. 0 aliLc i.: ll'.- j rt,.,, u.i r,, ;i !,;l r, ,l i . '1, o-J.i ' ],l 5, + ,',1i ntpl en;:.,:!!' l i i otl t'J,-r ",*;; g rowth p rob ler is ,s Ee ii] - [ t . 1, it r , { r ir , , 6 i( ; : , v i, " t " , *; " ; l l umbel C i .pl -,,f,:' rl r.,..r-1., ,,1';l ' ',19., z:i L -i ,i sr!-r!u !J !r nonlinear/(;r,y) ol tne iorr,r r,,:: .'i ,. -' , :, r:r:s6i 11ta ,; ;horv the el l l r.i r:r,i ', ani a,-,;rr. "r. !:ct l -,r. t, ;l i c1u':'. , ;.-,ttl :J ),' :i 'ai .-, ri el ; t l i nal l y, ' ' ' t r , > 1' , iutlr]ufizes '"ic ll*,'..:i ,u:Liii l.ii: ,, -.!t-- ''l ) !'.t'.' f(t,t') = ),TIL