Nature inspired computational technique for the numerical solution of nonlinear singular boundary value problems...

Area of Science:

• Physiological modeling
• Computational mathematics
• Numerical analysis

Background:

• Nonlinear singular boundary value problems are common in physiological modeling.
• Accurate numerical solutions are crucial for understanding physiological systems.
• Existing methods may face challenges with the complexity of these problems.

Purpose of the Study:

• To develop and validate a hybrid heuristic computing method for solving nonlinear singular boundary value problems in physiology.
• To utilize log sigmoid basis functions for approximate solutions.
• To optimize parameters using a combination of genetic, interior point, and active set algorithms.

Main Methods:

• A hybrid heuristic computing approach combining genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA).
• Employing log sigmoid basis functions to construct approximate solutions.
• Formulating a fitness function based on mean square error of the ordinary differential equation (ODE) and boundary conditions.

Main Results:

• The proposed method successfully solved three physiological examples.
• Obtained approximate solutions demonstrated excellent agreement with exact solutions.
• The hybrid method showed comparable or superior accuracy to conventional numerical solutions.

Conclusions:

• The hybrid heuristic computing method is efficient and viable for solving nonlinear singular boundary value problems in physiology.
• This approach offers a robust alternative for physiological modeling and simulation.
• The combination of optimization algorithms enhances the accuracy and reliability of the numerical solutions.