A Singular Initial Value Problem to Construct Density-Equalizing Maps
نویسندگان
چکیده
منابع مشابه
A Singular Initial Value Problem to Construct Density-equalizing Maps
The diffusion-based algorithm to produce density-equalizing maps interprets diffusion as an advection process. This algorithm uses the dynamics of a flow that is defined by an initial value problem that turns out to be very singular at the initial time. The singularities appear when the initial density has line or angle discontinuities, which is always the case, for example, in area cartogram m...
متن کاملReproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem
In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...
متن کاملDiffusion-based method for producing density-equalizing maps
Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale region...
متن کاملDensity-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps of simplyconnected open surfaces in R3. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properti...
متن کاملreproducing kernel hilbert space(rkhs) method for solving singular perturbed initial value problem
in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2011
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-011-9236-z