A new operational matrix based on Bernoulli polynomials

2014/08/10 by Jamal Amani Rad, Rad, J. A., Saeed Kazem +5
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1408.2207

openalex publication_date 2014/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This method can be used for many problems such as differential equations, integral equations and so on. Numerical examples show the method is computationally simple and also illustrate the efficiency and accuracy of the method.

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