Hashem Saberi Najafi - Faculty of mathematics, Guilan university,Iran
Azam Mokhtari Naseri - Faculty of mathematics ,Azad university of Lahijan,Iran

Many physical phenomena lead to parabolic initial boundary value problems with nonlocal boundary conditions , we consider a one dimensional heat equation subject to the specifications of mass , there are several methods for solution of it , for example FTCS(1,3) , BTCS(3,1) ,Crandall(3,3) , adapted scheme,…see( [9],[12],[11],[10] ). in [12] writer have introduced several adapted scheme for example (2,1) ,(3,1) ,(4,1) ,(5,1),…In this paper , weapply (5,1) adapted scheme that truncation error of it is o( 4 h ) for k = h in equal time and Space step size ,while methods in [9],[11],[10] are second order in time or space ,values of function have shows in Some tables. Also new scheme requires a smaller storage and CPU time employed than other algorithms.

nonlocal boundary value problems , Crandall formula , adapted scheme , numericalexample