scholarly journals A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

2020 ◽  
Vol 8 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Juan L. G. Guirao ◽  
Muhammad Shoaib
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Linear Boundary ◽  
Non Linear

Iterative bounds for the stable solutions of convex non-linear boundary value problems

1977 ◽  
Vol 76 (2) ◽  
pp. 81-94 ◽  
Author(s):  
J. W. Mooney ◽  
G. F. Roach
Keyword(s):  
Boundary Value Problems ◽  
Differential Expression ◽  
Boundary Value ◽  
Linear Boundary ◽  
Non Linear ◽  
Unstable Solutions ◽  
Neumann Type ◽  
Thermal Combustion ◽  
Stable Solutions ◽  
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SynopsisWe consider a class of convex non-linear boundary value problems of the formwhere L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.

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