Abstract: A high pricision combination method for solving BIE of the second kind is presented. The combination algorithm is as follows:Step 1. Compute the j^th(j=1,…,m) Nyström approximate equation with nodes {(nj+j)/(mn)}_i=1ⁿ parallelly. Step 2. Compute the j^th(j=1,…,m) interior print value by the j^th Nyström solution parallelly. Step 3. Compute the average of m interior point values, which is the combination approximation.It can be proved that the precision of the combination approximation is almost same as the precision of Nyström appximation with mn nodes.

Key words: boundary integral equation, Nyström method, compination method