A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
2018 ◽
Vol 26
(6)
◽
pp. 835-857
◽
Keyword(s):
Abstract We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method.
Keyword(s):
Keyword(s):
2000 ◽
Vol 112
(1)
◽
pp. 133-142
◽
1985 ◽
Vol 60
(1)
◽
pp. 1-20
◽
Keyword(s):
Keyword(s):
2008 ◽
Vol 1
(3)
◽
pp. 205
◽
Keyword(s):