A collocation method with the modified equilibrium on line method (ELM) forimposition of Neumann and Robin boundary conditions is presented for solving the two-dimensionalacoustical problems. In the modified ELM, the governing equations are integrated over the lines onthe Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. Inother words, integration domains are...

The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...

By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...

The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.

We are interested in a nonlinear boundary value problem for (|u′′|p−2u′′)′′ = λ|u|p−2u in [0,1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n− 1 zero points in (0,1). Eigenvalues of the ...

Extending the previous work on the corresponding inverse Dirichlet problem, we present a factorization method for the solution of an inverse Neumann boundary value problem for harmonic vector fields. 2000 Mathematics Subject Classification: 31B10, 31B20, 45A05, 45Q05, 78A30.

We clarified the variational meaning of the special values ζ(2M) (M = 1, 2, 3, · · · ) of Riemann zeta function ζ(z). These are essentially the best constants of five series of Sobolev inequalities. In the background, we consider five kinds of boundary value problem (periodic, antiperiodic, Dirichlet, Neumann, Dirichlet-Neumann) for a differential operator (−1) (d/dx) . Green functions for thes...