In this paper a new meshless method for eigenproblems with Laplace and biharmonic operators in simply and multiply connected domains is presented. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. These problems are solved using the method of fundamental solutions. The method presented shows a high precision in simply and multiply connected domains. The results of the numerical experiments justifying the method are presented.
S. Reutskiy, "The method of fundamental solutions for eigenproblems with laplace and biharmonic operators," Computers, Materials & Continua, vol. 2, no.3, pp. 177–188, 2005.
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