The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations (L. Fox)

SIAM Review ◽  
1959 ◽  
Vol 1 (2) ◽  
pp. 177-178
Author(s):  
G. T. Thompson
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Point Boundary ◽  
Boundary Problems

POST ADAPTATION FOR A NUMERICAL SOLUTION OF THE SPHERICALLY-SYMMETRIC RIEMANN PROBLEM

1990 ◽  
Vol 01 (04) ◽  
pp. 285-298
Author(s):  
B. YUDANIN ◽  
M. LAX
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Riemann Problem ◽  
General Purpose ◽  
Spherically Symmetric ◽  
Lagrangian Coordinates ◽  
Point Boundary ◽  
Boundary Values

A"folding" transformation is used to reduce a two point boundary value problem to one point boundary values (with double the number of functions). A transformation to quasi-Lagrangian coordinates is used to transform discontinuities to rest. After these transformations the general purpose numerical package POST (partial and ordinary differential equations solver in time and one space coordinates) can be successfully applied to a system of hydrodynamical equations, whose solution exhibits jumps and cusp-type discontinuities. Numerical results are presented for the spherically-symmetric shock problem.

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