Mikhlin’s Integral Equation and the Integral Equation with the Generalized Neumann Kernel on Simply Connected Domains

Algorithm 1

Solving the Dirichlet problem with Mikhlin’s integral equation method

Step 1. Solve the integral equation (25) for .

Step 2. Find the boundary values of given in equation (35).

Step 3. Compute the values of for using (49).

Step 4. Finally, evaluate the solution through .