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Optimal Uniform Finite Difference Scheme For The Scalar Singularly Perturbed Riccati  Equation

K.Selva Kumar

Department of Mathematics, Anna University of  Technology, Tirunelveli - 627007,  Tamil Nadu, India.  E-mail: k_selvakumar10@yahoo.com

 

 

 

ABSTRACT                                                                 

               A finite difference scheme of order one is presented for the scalar singularly Perturbed    Riccati equation

                               ε u'(x) = c(x) u2 (x)+d (x)u(x)+ e(x), x >  0 , u (0) = φ  

 with a small parameter  ε multiplying the first  derivative. The scheme is derived from Euler’s Backward Rule.  And the scheme satisfies error estimate of the form                                                          | u (xi ) – ui | ≤  C min  ( h , ε ) ,

where  C is  independent of  i , h  and  ε.   Here  h is the  mesh size  and xi  is any mesh point.  The scheme presented in this  paper is new and it is different from the uniform schemes of  order one available in the literature.  Finally  numerical experiments are presented.

 Running Head :   Fitted finite difference scheme

 

 

 

 

 


International eJournal of Mathematical Sciences, Technology and Humanities

Volume 2, Issue 2, Pages:  370 - 382