Daniel Lesnic

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In this paper, the iterative algorithm proposed by Kozlov et al. [Comput. Maths. Math. Phys. 31 (1991) 45] for obtaining approximate solutions to the ill-posed Cauchy problem for the Helmholtz equation is analysed. The technique is then numerically implemented using the boundary element method (BEM). The numerical results confirm that the iterative BEM(More)
In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of(More)
The analytical solutions for linear, one-dimensional, time-dependent partial differential equations subject to initial or lateral boundary conditions are reviewed and obtained in the form of convergent Adomian decomposition power series with easily computable components. The efficiency and power of the technique are shown for wide classes of equations of(More)