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The Dirichlet problem for Laplace's equation in an area between two arbitrary profiled infinitely long cylinders is rigorously solved by the Method of Regularization. The obtained solution is applied to the accurate analysis of the shielded microstrip line with homogeneous dielectric filling and thick conductor - the structure supporting the transmission of an ideal TEM-wave. Capacitance and characteristic...
The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain bounded by closed curves and open arcs is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. It means, that the solution can be computed by standard codes.
The Laguerre transform with respect to the time variable has been applied to the Dirichlet problem for the wave equation. Received system of elliptic boundary value problems has been numerically solved with the boundary elements method. Transformants of the time-dependent solution have been represented in form of a simple layer potentials, which densities are determined recurrently from a boundary...
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