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
jth(
j=1,…,
m) Nyström approximate equation with nodes (
nj+
j)/(
mn)
i=1n parallelly. Step 2. Compute the
jth(
j=1,…,
m) interior print value by the
jth 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.