# Perturbation Expansion for Solving the Fixed Gravimetric Boundary Value Problem

• Roland Klees
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 114)

## Abstract

One of the most characteristic features of nearly all geodetic boundary value problems is their non-linearity. This property is caused either by our insufficient knowledge of the geometry of the boundary surface or by the boundary condition, which usually is a non-linear functional of the gravitational potential, whereas the partial differential operator is almost linear. All numerical methods, however, which have been considered up to now are restricted to linear boundary value problems (bvp). Therefore, we are faced with mainly three problems:
1. 1.

the linearization of the non-linear bvp around an approximate solution,

2. 2.

the solution of the related linear bvp, and

3. 3.

the construction of a convergent iteration method to solve the non-linear problem by iteration, i.e. by solving a family of related linear problems.

## Keywords

Implicit Function Theorem Single Layer Potential Geodetic Boundary Centrifugal Potential Oblique Boundary
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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