ASYMPTOTIC METHOD FOR SINGULAR PERTURBATION PROBLEM OF ORDINARY DIFFERENCE EQUATIONS

This paper is taken up for the following difference equation problem(P,)(L,y)≡εy(k+1)+a(k,ε)y(k)+b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1),By≡-y(0)+cy(1)=a,By≡-cy(N-1)+y(N)=βwhereεis a small parameter,c,c,a,βconstants and a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)functions of k andε.Firstly,the case with constant coefficients isconsidered.Secondly,a general method based on extended transformation is given tohandle(P.)where the coefficients may be variable and uniform asymptotic expansionsare obtained Finally,a numerical example is provided to illustrate the proposed method.