scholarly journals Numerical solution of singular boundary value problems using Green’s function and Sinc-Collocation method

2020 ◽  
Vol 32 (7) ◽  
pp. 2962-2968
Author(s):  
Z. Balali ◽  
J. Rashidinia ◽  
N. Taheri
Keyword(s):  
Green’S Function ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Green's Function ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems

scholarly journals Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Suheel Abdullah Malik ◽  
Ijaz Mansoor Qureshi ◽  
Muhammad Amir ◽  
Ihsanul Haq
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Fitness Function ◽  
Boundary Value ◽  
Computational Technique ◽  
Singular Boundary ◽  
Interior Point Algorithm ◽  
Singular Boundary Value Problems ◽  
Hybrid Heuristic

We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

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