Stability and Accuracy of a Class of Numerical Boundary Conditions for the Advection Equation

Elvius & Sundstrm (1973) have used a stable time averagedboundary condition with the leap-frog scheme for the numericalsolution of hyperbolic partial differential equations. Gary(1978) generalized the time averaged boundary condition by includinga scalar parameter. This paper examines the stability and accuracyof the more general boundary condition. A stability intervalis found for the scalar parameter and an optimum value of theparameter is obtained which minimizes the boundary errors. Numericalexperiments are described which support the theoretical predictions.     

Quadrature methods for logarithmic-kernel integral equations on closed curves

The recently proposed method of Sloan and Burn for the logarithmic-kernelfirst-kind integral equation on closed curves is modified, soas to permit high-order convergence in appropriate negativenorm even when the solution is not smooth. In addition, theresult of Sloan and Burn for the original method is shown tobe exrtendable from circular to general smooth curves withoutloss.