Tracing the buckling of a rectangular plate with the Block GMRES method

We investigate bifurcation scenario of the von Kلrmلn equations with partially clamped boundary conditions defined in rectangular domains. First, we study how the (preconditioned) Block GMRES method can be used in the context of continuation methods for tracing solution curves of large systems of nonlinear equations. Next, we discuss linear stabilities of the von Kلrmلn equations with partially clamped boundary conditions. In particular, we calculate the first seven eigenvalues and its associated eigenfunctions of the linearized von Kلrmلn equations via computer algebra. The Block GMRES method is used to solve linear systems and to detect singularity along solution paths of the discrete problem. Sample numerical results are reported.