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.