The stability of the Nyström method for double layer potential equations
Provides theoretical stability criteria for a numerical method used in potential theory, relevant to researchers in computational mathematics and integral equations.
The paper establishes necessary and sufficient conditions for the stability of the Nyström method for double layer potential equations on piecewise smooth contours, showing that stability depends on invertibility of operators related to corner opening angles. Numerical experiments confirm that certain opening angles cause instability.
The stability of the Nyström method for the double layer potential equation on simple closed piecewise smooth contours is studied. Necessary and sufficient conditions of the stability of the method are established. It is shown that the method under consideration is stable if and only if certain operators associated with the opening angles of the corner points are invertible. Numerical experiments show that there are opening angles which cause instability of the method.