Abstract: In this paper we consider the Dirichlet problem for elliptic differential equations. A special difference scheme is constructed from the necessary condition of uniform convergence. We also prove the uniform convergence and the asymptotic behavior of the solution of the difference problem, and give the error estimate.

Key words: elliptical sandwich plate, superpositive-iterative harmonic balance (SIHB) method, 1/3 subharmonic solution, bifurcation