Methods for solving one-dimensional boundary-value problems in a nonlinear elastic medium

1996 ◽  
Vol 114 (1-4) ◽  
pp. 51-69 ◽  
Author(s):  
Yu. A. Rossikhin ◽  
M. V. Shitikova
Keyword(s):  
Boundary Value Problems ◽  
Elastic Medium ◽  
Boundary Value ◽  
One Dimensional ◽  
Nonlinear Elastic Medium ◽  
Dimensional Boundary ◽  
Nonlinear Elastic

scholarly journals The HK-Sobolev space and applications to one-dimensional boundary value problems

2020 ◽  
Vol 32 (6) ◽  
pp. 2790-2796
Author(s):  
T. Pérez-Becerra ◽  
S. Sánchez-Perales ◽  
J.J. Oliveros-Oliveros
Keyword(s):  
Sobolev Space ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
One Dimensional ◽  
Dimensional Boundary

FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350082 ◽  
Author(s):  
RAFAEL G. CAMPOS ◽  
RAFAEL GARCÍA RUIZ
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Kdv Equation ◽  
Boundary Value ◽  
Soliton Solutions ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Dimensional Boundary ◽  
The Fourier Transform ◽  
Derivatives Of

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

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