Numerical verification of solutions for obstacle problems using a Newton-like method

This paper is a continuation of the preceding study [1] in which we described a method which automatically proves the existence of solutions for variational inequalities by computer. We newly formulate a verification method using a Newton-like method. This approach enables us to remove the restriction in the previous paper to the retraction property of the operator in a neighborhood of the solution. We show some numerical examples which confirm that the method is really applicable to problems which have no retraction property. (C) 2000 Elsevier Science Ltd. All rights reserved.