Multiple Reciprocity Method for Buckling Eigenvalue Problem and Its Convergence Analysis

The multiple reciprocity method for buckling eigenvalue problem is discussed. Compared with other problems, Laplace operator and biharmonic operator are contained in the control equation of the buckling eigenvalue problem, so we must introduce two series of high-order fundamental solution sequences. Using them we can proceed multiple replacements. Then MRM boundary integral expression and MRM boundary integral equation are obtained, and the error estimates, which is the approximate solution of the equation is given. These works provide wide methods and theoretical basis for studying buckling eigenvalue problem.