Abstract
In this paper the new integral equation method proposed and developed in our previous papers on boundary-value problems is applied to eigenvalue problems. Two formulations by the integral equation expression are performed from the same manner that we adopted on the boundary value problems. As the result, whether the derived integral equation is single or not, the integral kernels do not include the unknown eigen-parameter. Through this notable feature in contrast with the boundary integral equation method, eigenvalue problems on continuous fields can be reduced to the standard eigenvalue problems of matrix equation. Finally, in order to show the applicability and validity of the proposed methodology and procedure, numerical calculations are performed for three illustrative examples, which are eigenvalue problems of Sturm-Liouville type equation, Helmholtz equation and biharmonic type equation. The approximate values of an eigenvalue parameter of each problem demonstrate a sufficient accuracy through the comparison of another values.
