Download or read book Linear Solutions of the Geodetic Boundary value Problem written by Helmut Moritz and published by . This book was released on 1968 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geodetic Boundary Value Problem the Equivalence between Molodensky s and Helmert s Solutions written by Fernando Sansò and published by Springer. This book was released on 2016-11-09 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new approach to interpreting the geodetic boundary value problem, successfully obtaining the solutions of the Molodensky and Stokes boundary value problems (BVPs) with the help of downward continuation (DC) based methods. Although DC is known to be an improperly posed operation, classical methods seem to provide numerically sensible results, and therefore it can be concluded that such classical methods must in fact be manifestations of different, mathematically sound approaches. Here, the authors first prove the equivalence of Molodensky’s and Stoke's approaches with Helmert’s reduction in terms of both BVP formulation and BVP solutions by means of the DC method. They then go on to show that this is not merely a downward continuation operation, and provide more rigorous interpretations of the DC approach as a change of boundary approach and as a pseudo BVP solution approach.
Download or read book Linear solutions of the geodetic boundaryvalue problem written by Helmut Moritz and published by . This book was released on 1968 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Download or read book Model Computations for Different Solutions of the Geodetic Boundary value Problem written by Joseph E. Gross and published by . This book was released on 1968 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Model Computations for Different Solutions of the Geodetic Boundary value Problem written by Karl-Rudolf Koch and published by . This book was released on 1968 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: To solve the boundary-value problem of physical geodesy, the perturbing potential is usually expressed by the potential of a simple layer. By introducing this expression into the boundary condition, Molodensky's basic integral equation is obtained; the solution of which enables us to compute the perturbing potential and its first derivative. To check the results of this method, Green's formula can be used. After transforming this formula and its derivative by a method, due to Molodensky, a linear integral equation for the disturbing potential is obtained. With the solutions of this integral equation, the first derivative of the disturbing potential can be computed from the transformed derivative of Green's formula. For a model consisting of a cone on a plane the basic integral equation and the integral equation of Green's formula are solved by successive approximation with a computer. The solution of the basic integral equation is also obtained by Molodensky's method. These three solutions are compared for different inclination angles of the surface of the cone. The results agree very well for small inclination angles, but the approximations don't converge for greater inclination angles. The reason has to be sought in the errors of numerical integration, by which the integration over the surface of the model is solved. (Author).
Download or read book The Geodetic Boundary Value Problem in Two Dimensions and Its Iterative Solution written by Martin van Gelderen and published by . This book was released on 1991 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geodetic Boundary Value Problems in View of the One Centimeter Geoid written by Fernando Sansò and published by Springer. This book was released on 1997-06-25 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: The precise determination of the figure of the earth and its exterior gravitational field requires the solution of the geodetic boundary value problem (GBVP). Recently, a whole series of new measurement techniques has became available, in particular air- and spaceborne methods. They will make its solution much more complete and accurate and will contribute to a better understanding of ocean circulation and of the earth's interior. The book consists of contributions from leading scientists presented at an international summer school. It covers all aspects of the solution of the GBVP, from a mathematical basis via geodetic modeling to its relationship with advanced measurements. It provides three foundations to determine the geoid at a 1-cm precision level.
Download or read book Geodetic Boundary Value Problem written by Fernando Sansò and published by . This book was released on 2017 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geodetic Boundary Value Problem in Two Dimensions and Its Iterative Solution written by Martin van Gelderen and published by . This book was released on 1991 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geodetic Boundary Value Problems in View of the One Centimeter Geoid written by Fernando Sansò and published by Springer. This book was released on 2014-03-12 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The precise determination of the figure of the earth and its exterior gravitational field requires the solution of the geodetic boundary value problem (GBVP). Recently, a whole series of new measurement techniques has became available, in particular air- and spaceborne methods. They will make its solution much more complete and accurate and will contribute to a better understanding of ocean circulation and of the earth's interior. The book consists of contributions from leading scientists presented at an international summer school. It covers all aspects of the solution of the GBVP, from a mathematical basis via geodetic modeling to its relationship with advanced measurements. It provides three foundations to determine the geoid at a 1-cm precision level.
Download or read book Nonlinear Solutions of the Geodetic Boundary Value Problem written by Helmut Moritz and published by . This book was released on 1969 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete series solution of Molodensky's boundary value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient. This equivalence gives a physical explanation of the divergence of the Molodensky series. The exclusion of topographic masses to improve convergence is discussed, and computational formulas for height anomalies and deflections of the vertical are given. In the Appendix, structural similarities between the series of celestial mechanics and of physical geodesy are used to get an insight into the convergence behavior of these series. Another argument for the divergence of series of Molodensky type is given. (Author).
Download or read book Boundary Value Problems Of Linear Partial Differential Equations For Engineers And Scientists written by Shien Siu Shu and published by World Scientific. This book was released on 1987-09-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised version of the author's lecture notes in a graduate course of applied mathematics. It is based on the idea that it may be more interesting to learn mathematics through the introduction of concrete examples. The materials are organised in a logical order that transmits the package of mathematical knowledge and methods to the students in an efficient manner.
Download or read book On the Linearized Boundary Value Problems of Physical Geodesy written by Bernhard Heck and published by . This book was released on 1991 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems written by Chi Yeung Lo and published by World Scientific. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.
Download or read book Solving Ordinary and Partial Boundary Value Problems in Science and Engineering written by Karel Rektorys and published by CRC Press. This book was released on 1998-10-20 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubíček and published by Prentice Hall. This book was released on 1983 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
