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

Abstract

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.

Numerical solution to nonlinear biochemical reaction model using hybrid polynomial basis differential evolution technique

“…To obtain the numerical solution of biochemical reaction model (7) and (8) The values of unknown parameters ( ) in (10) - (13) are determined by formulating a trial solution of the given problem using a fitness function ( ) given by (14) where j is the cycle index, and represent the mean square errors associated with the system of coupled nonlinear ODEs (7) and (8) respectively, given as follows…”

“…The FF function given by (14) contains the unknown adaptable coefficients ( , . The minimization of fitness function ( is carried out by employing the evolutionary algorithms GA and DE for acquiring the unknown parameters.…”

“…In recent years many authors have used nature and biologically inspired based computation techniques as an alternative for solving nonlinear ODEs arising in diverse fields of engineering and science [6][7][8][9][10][11][12][13][14][15][16]. Very recently Malik et al [6,7] employed heuristic technique based on hybrid genetic algorithm for numerically solving the nonlinear singular boundary value problems in physiology and the Bratu problem.…”

“…Very recently Malik et al [6,7] employed heuristic technique based on hybrid genetic algorithm for numerically solving the nonlinear singular boundary value problems in physiology and the Bratu problem. Arqub et al [8] used genetic algorithm (GA) based method for solving linear and nonlinear singular boundary value problems (BVPs).…”

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

“…In recent years, many authors have used heuristic computation based techniques for solving variety of differential equations [ 25 – 35 ]. Very recently Malik et al [ 25 , 26 ]used nature inspired computation based approach for solving systems of nonlinear ordinary differential equations (NODEs), including biochemical reaction model [ 25 ], and boundary value problems arising in physiology [ 26 ]. Khan et al[ 27 ] used evolutionary computation (EC) based artificial neural network (ANN)method for solving van der pol oscillator equation.…”