REuuE D'ANALYSE NUMÉRIQUE ET DE THÉORID DE L'APPROXIMATION roME XXVII, No 2, 1g9g, pp. 297_308 T}M APPRO)üMATION BY SPLINE FTINCTIONS OF THE SOLUTION OF A SINGULARLY PERTIIRBED BILOCAL PROBLEM

C Mustãta, A Mure$, R Mustãta
unpublished
lems admit exact solutions having both are thin transition layers wheõ the We define a class of spli these problems and obtain suffi oscillations on the subintervals Let n23, n e [!, and let (1) Âr:-oo=/_r (a=to1tt1,..1tr=þ(/r*,:*co a division ofthe real axis. Denote bV 4(Â,) the set of functions .r: R + R verifuing the conditions: 1" s e C4(R); 2" sltt e'4, It, =[,tt-t,ttr), k=1,2,...,n; 30 slro e'4,slL,*,.%, Io =lt ¡,t0), In+t =ft*t,*t), where Q, denotes the set of polynomials of degree z. As
more » ... als of degree z. As concems the behavior of functions in this class, one can prove TiÐoREM l. Everyfunction s Ë nZ(Ar) can be written in theform .ç(/)= f u", n,L oo(t-tÐj, / e [R, ,=0 k=0 where (3) t oo =0, f oo,o =0, k =0 k=0 I AMS Ctassification Code: 34815. 34A50.
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