ESTIMATION OF THE CONVERGENCE RATE OF SCHWARZ ALTERNATING METHOD AND AN ACCELERATED ALGORITHM

This paper examines the relationship between the overlapping ways of s ubdomains and the convergence rate in the solution of elliptic partial differential equations by the Schwarz alternating method. An accelera ted Schwarz method is constructed and a linearization technique for se mi-linear equations, which has a convergence rate equal to that for li near equations, is designed. In addition, the application of the Schwa rz algorithm to the solution of biharmonic equations is discussed.