Improperly Posed Problems in Partial Differential Equations

Payne, L. E.

doi:10.1137/1.9781611970463

Cited by 288 publications

(127 citation statements)

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“…As the downward continued gravity anomaly on the sphere is the unknown under the integral, the formula is a Fredholm integral equation of the first kind and the problem is improperly posed (e.g., Payne 1975 andHansen 1998). In the present case this implies that a detailed solution will be sensitive to errors in the data, and the propagated uncertainty will increase with topographic elevation and the resolution requested for the solution.…”

Section: The Dwc Effect In the Rcr Techniquementioning

confidence: 99%

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

Ligas

2013

Journal of Geodetic Science

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Abstract:The paper presents a solution to one of the basic problems of computational geodesy -conversion between Cartesian and geodetic coordinates on a biaxial ellipsoid. The solution is based on what is known in the literature as "latitude equation". The equation is presented in three different parameterizations commonly used in geodesy -geodetic, parametric (reduced) and geocentric latitudes. Although the resulting equations may be derived in many ways, here, we present a very elegant one based on vectors orthogonality. As the "original latitude equations" are trigonometric ones, their representation has been changed into an irrational form after Fukushima (1999Fukushima ( , 2006. Furthermore, in order to avoid division operations we have followed Fukushima's strategy again and rewritten the equations in a fractional form (a pair of iterative formulas). The resulting formulas involving parametric latitude are essentially the same as those introduced by

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Section: The Dwc Effect In the Rcr Techniquementioning

confidence: 99%

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

Ligas

2013

Journal of Geodetic Science

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“…This problem and its generalizations have received considerable attention in the literature [17,21]. In this section, we propose to trace numerically the motion of the singularities in the complex plane as the parameter a varies.…”

Section: Locating Singularities: First Examplementioning

confidence: 99%

Deciphering singularities by discrete methods

Tourigny¹,

Grinfeld²

1994

Math. Comp.

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“…One of the problems with Young's results is that all of the kt's are required to have the same sign. Ames [3] oversomes this difficulty by using a logarithmic convexity argument [10]. However, in order to do this, Ames needs strong requirements placed on the function at the face x, = 0 if k¡ < -1 in that uux must approach zero faster than xk>.…”

Section: Uniqueness For Singular Backward Parabolic Inequalities Alanmentioning

confidence: 99%