On boundary conditions for the numerical solution of hyperbolic differential equations

1980 ◽  
Vol 15 (8) ◽  
pp. 1113-1127 ◽  
Author(s):  
D. M. Sloan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Hyperbolic Differential Equations

scholarly journals Collocation for High-Order Differential Equations with Lidstone Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Francesco Costabile ◽  
Anna Napoli
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Collocation Method ◽  
Numerical Experiments ◽  
Recurrence Formula ◽  
High Order ◽  
Theoretical Results

A class of methods for the numerical solution of high-order differential equations with Lidstone and complementary Lidstone boundary conditions are presented. It is a collocation method which provides globally continuous differentiable solutions. Computation of the integrals which appear in the coefficients is generated by a recurrence formula. Numerical experiments support theoretical results.

scholarly journals Derivation of boundary conditions for the artificial boundaries associated with the solution of certain time dependent problems by Lax–Wendroff type difference schemes

1982 ◽  
Vol 25 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Wilson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Time Dependent ◽  
Finite Region ◽  
Partial Differential ◽  
Artificial Boundaries ◽  
Fixed Boundaries ◽  
Time Dependent Problems

Many problems involving the solution of partial differential equations require the solution over a finite region with fixed boundaries on which conditions are prescribed. It is a well known fact that the numerical solution of many such problems requires additional conditions on these boundaries and these conditions must be chosen to ensure stability. This problem has been considered by, amongst others, Kreiss [11, 12, 13], Osher [16, 17], Gustafsson et al. [9] Gottlieb and Tarkel [7] and Burns [1]

A non-linear analysis of corrugated plates, closed cylinders, and developable shells with parallel generators

1970 ◽  
Vol 5 (4) ◽  
pp. 292-301
Author(s):  
R W Gaisford ◽  
B H Baines
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Linear Analysis ◽  
Not Given ◽  
Non Linear ◽  
Simplifying Assumptions ◽  
The Subject ◽  
Corrugated Plates ◽  
Experimental Comparisons

A set of non-linear simultaneous differential equations is developed which describes the behaviour of certain types of highly curved shells. Certain simplifying assumptions are made for which justifying arguments are put forward and the resulting equations remain generally applicable within wide limits of initial shell curvature and of deformation. Boundary conditions are developed for a number of simple cases and the methods available for the numerical solution of the equations are briefly discussed. Experimental comparisons and detailed descriptions of numerical procedures are not given here but will be the subject of a further paper.

Stress and Displacement Analysis of a Shell Intersection

1970 ◽  
Vol 92 (2) ◽  
pp. 303-308 ◽  
Author(s):  
K. C. Pan ◽  
R. E. Beckett
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Numerical Solution ◽  
Numerical Computation ◽  
Cylindrical Shells ◽  
Numerical Results ◽  
Radius Ratio ◽  
Displacement Analysis

The problem of two normally intersecting cylindrical shells subjected to internal pressure is considered. The differential equations used for the shells are solved subject to the boundary conditions imposed along the intersection between the two cylinders. Details of a procedure for obtaining a numerical solution are given. Numerical results for a radius ratio of 1:2 are presented. Problems encountered in the numerical computation are discussed and the results of the analysis are compared with experiment.

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