Finite difference approximations for a class of non-local parabolic equations
1997 ◽
Vol 20
(1)
◽
pp. 147-163
◽
Keyword(s):
In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fully-implicit scheme also possesses strict monotonicity. It is also proved that finite difference solutions approach to zero ast→∞exponentially. The numerical results of some examples are presented, which support our theoretical justifications.
Explicit finite difference methods for two-dimensional diffusion with a non-local boundary condition
1994 ◽
Vol 32
(11)
◽
pp. 1829-1834
◽
1976 ◽
Vol 2
(1)
◽
pp. 23-26
◽
2021 ◽
Vol 13
(2)
◽
pp. 57-71
1999 ◽
Vol 106
(2)
◽
pp. 255-269
◽
1976 ◽
Vol 53
(3)
◽
pp. 644-668
◽
1988 ◽
1991 ◽
Vol 93
(1)
◽
pp. 108-127
◽