scholarly journals Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. II. The evolution equations

1998 ◽  
Vol 58 (6) ◽  
Author(s):  
Jörg Frauendiener
Keyword(s):  
Initial Value Problem ◽  
Evolution Equations ◽  
Einstein Equations ◽  
Numerical Treatment ◽  
Initial Value ◽  
Vacuum Einstein Equations

Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations

1990 ◽  
Vol 427 (1872) ◽  
pp. 221-239 ◽  
Keyword(s):  
Cauchy Problem ◽  
Perfect Fluid ◽  
Initial Value Problem ◽  
Einstein Equations ◽  
Initial Value ◽  
Fluid Source ◽  
Null Hypersurfaces ◽  
The Cauchy Problem ◽  
Well Posed ◽  
Characteristic Initial Value Problem

A method is described by means of which the characteristic initial value problem can be reduced to the Cauchy problem and examples are given of how it can be used in practice. As an application it is shown that the characteristic initial value problem for the Einstein equations in vacuum or with perfect fluid source is well posed when data are given on two transversely intersecting null hypersurfaces. A new discussion is given of the freely specifiable data for this problem.

Numerical treatment of a quasilinear initial value problem with boundary layer

2015 ◽  
Vol 93 (11) ◽  
pp. 1845-1859
Author(s):  
Musa Cakir ◽  
Erkan Cimen ◽  
Ilhame Amirali ◽  
Gabil M. Amiraliyev
Keyword(s):  
Boundary Layer ◽  
Initial Value Problem ◽  
Numerical Treatment ◽  
Initial Value
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