A numerical approach for the solution of a class of singular boundary value problems arising in physiology

作者：Mohsenyzadeh Mohamadreza; Maleknejad Khosrow^*; Ezzati Reza

来源：Advances in Difference Equations, 2015, 2015(1): 231.

DOI：10.1186/s13662-015-0572-x

• orthonormal Bernoulli polynomials
• differential operational matrix
• physiology problems

The purpose of this paper is to introduce a novel approach based on the operational matrix of orthonormal Bernoulli polynomial for the numerical solution of the class of singular second-order boundary value problems that arise in physiology. The main thrust of this approach is to decompose the domain of the problem into two subintervals. The singularity, which lies in the first subinterval, is removed via the application of an operational matrix procedure based on differentiating that is applied to surmount the singularity. Then, in the second subdomain, which is outside the vicinity of the singularity, the resulting problem is treated via employing the proposed basis. The performance of the numerical scheme is assessed and tested on specific test problems. The oxygen diffusion problem in spherical cells and a nonlinear heat-conduction model of the human head are discussed as illustrative examples. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

• 出版日期2015-7-25