scholarly journals Numerical Solution for Singular Boundary Value Problems Using a Pair of Hybrid Nyström Techniques

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 202
Author(s):  
Mufutau Ajani Rufai ◽  
Higinio Ramos
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Physical Model ◽  
Chemical Kinetics ◽  
Boundary Value ◽  
Test Problems ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Integration Interval ◽  
Fundamental Properties

This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.

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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