An effective approach for solving a class of nonlinear singular boundary value problems arising in different physical phenomena

2021 ◽  
pp. 1-18
Author(s):  
Saurabh Tomar
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Physical Phenomena

scholarly journals Comments on the use of block methods for solving singular boundary value problems

2020 ◽  
Vol 34 ◽  
pp. 01005
Author(s):  
Higinio Ramos
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Block Method ◽  
Integration Interval ◽  
Equation Modelling ◽  
Block Methods ◽  
Physical Phenomena ◽  
Thermal Explosion Theory

Singular boundary-value problems appear frequently on the modellization of many physical phenomena as in catalytic diffusion reactions, chemical kinetics, thermal-explosion theory, or electro hydrodynamics, among others. The singular Lane-Endem equation is a typical kind of equation modelling some of those problems. Unfortunately, just in few occasions the exact solutions can be obtained. In this situation the block methods have been used largely for approximating different kind of differential problems. We propose its use for solving singular boundary value problems. The proposed strategy consist in a block method combined with an appropriate set of formulas which are developed at the first subinterval to circumvent the singularity at the left end of the integration interval. Some examples are presented to validate the efficiency of the proposed strategy.

scholarly journals A Galerkin method ofO(h2)for singular boundary value problems

2002 ◽  
Vol 29 (6) ◽  
pp. 361-369
Author(s):  
G. K. Beg ◽  
M. A. El-Gebeily
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Basis Functions ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Special Basis

We describe a Galerkin method with special basis functions for a class of singular two-point boundary value problems. The convergence is shown which is ofO(h2)for a certain subclass of the problems.

Sign in / Sign up

Export Citation Format

Share Document