Abstract: General Ray (GR) method for solution of the Dirichlet boundary value problems for the Laplace type equation with variable coefficient is proposed. The method is based on reduction of Partial Differential Equation (PDE) to assemblage of Ordinary Differential Equations (ODE) using local traces for considered functions and operators. GR-method presents the solution of the Dirichlet boundary value problem for this type of equations by explicit analytical formulas that use the direct and inverse Radon transform. Proposed version of GR-method is justified theoretically, realized as stable algorithms and program package in MATLAB system. The quality of constructed software is demonstrated by numerical experiments. Applications to the stationary problems of electrodynamics and HEAT TRANSFER thermo conductivity are discussed.
 

Brief Biography of the Speaker: Grebennikov Alexander Ivanovich was born at 17 of April 1950 in Gorky city, Russia. The student of the Faculty of Calculating Mathematics and Cybernetics (FCMC) of Gorky State University at 1967-1972. Postgraduate student of the FCMC of Moscow State University (MSU) at 1972-1975. Was graduated PhD in 1976. Scientific interests: splines; data processing; inverse and ill-posed problems; fast algorithms in numerical analysis and applications. Publications: more than 120 articles in journals and proceedings, 2 texts of lectures, 5 monographs. Work: assistant professor of the FCMC MSU at 1976-1989; senior staff scientist of Scientific Research Computing Center (SRCC) MSU at 1989-1994; Head of Laboratory in SRCC MSU at 1995-1999; full professor of the Faculty of Physic and Mathematic Sciences of Autonomous University of Puebla, Mexico from 1999 to present day. Adres: Av. San Claudio y Río verde, Ciudad Universitaria, FCFM, CP 72570, Puebla, tel./fax (52 222) 8920073, e-mail: agrebe@fcfm.buap.mx