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A Guide to Concentration Alternating Frequency Response Analysis of Fuel Cells

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Bernstein collocation method for neutral type functional differential equation.

¹Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia.

Mathematical Biosciences and Engineering : MBE

|April 24, 2021

Summary

This study introduces a spectral collocation method using Bernstein polynomials for neutral type functional differential equations. A basis transformation to Legendre polynomials enhances accuracy and efficiency in finding approximate solutions.

Keywords:

Bernstein collocation method convergence analysis functional differential equation numerical examples

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Area of Science:

Mathematics
Numerical Analysis

Background:

Functional differential equations of neutral type are challenging due to their dependence on the function's history.
Explicit solutions are often impossible, necessitating numerical approximation techniques.

Purpose of the Study:

To develop an efficient and accurate numerical method for solving functional differential equations of neutral type.
To address the limitations of Bernstein polynomials in spectral collocation methods.

Main Methods:

A spectral collocation method based on Bernstein polynomials was employed.
A change of basis transformation from Bernstein to Legendre polynomials was utilized to leverage the properties of orthogonal polynomials.
Error analysis in the infinity norm was performed.

Main Results:

The proposed method, enhanced by the Bernstein-Legendre basis transformation, demonstrated efficiency and accuracy.
Numerical examples validated the effectiveness of the scheme.

Conclusions:

The spectral collocation method with a Bernstein-Legendre basis transformation provides a robust approach for approximating solutions to neutral type functional differential equations.
This technique overcomes the orthogonality limitations of Bernstein polynomials, leading to improved computational performance.