Solution of a non-linear discrete boundary value problem by a continuous analog of Newton's method

1969 ◽  
Vol 9 (2) ◽  
pp. 254-262
Author(s):  
E.P. Zhidkov ◽  
I.V. Puzyni
Keyword(s):  
Boundary Value Problem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Boundary Value ◽  
Continuous Analog ◽  
Discrete Boundary Value Problem ◽  
Non Linear

scholarly journals APPLICATION OF PROJECTION ALGORITHMS TO DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS

2019 ◽  
Vol 61 (1) ◽  
pp. 23-46 ◽  
Author(s):  
BISHNU P. LAMICHHANE ◽  
SCOTT B. LINDSTROM ◽  
BRAILEY SIMS
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Newton’S Method ◽  
Newton's Method ◽  
Boundary Value ◽  
Second Order ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
The Stability

The Douglas–Rachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary value problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well suited to parallelization. We explore the stability of the method by applying it to several BVPs, including cases where the traditional Newton’s method fails.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

Existence of Two Solutions for a Second-Order Discrete Boundary Value Problem

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Pasquale Candito ◽  
Giovanni Molica Bisci
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Discrete Boundary Value Problem

AbstractThe existence of two nontrivial solutions for a class of nonlinear second-order discrete boundary value problems is established. The approach adopted is based on variational methods.

Sign in / Sign up

Export Citation Format

Share Document