A new operational matrix based on Bernoulli polynomials
This provides a new computational tool for solving differential and integral equations, but the improvement over existing polynomial-based methods is not quantified.
The authors introduce Bernoulli polynomials and construct operational matrices for integration, derivative, and product, then use them to convert differential equations into algebraic systems. Numerical examples demonstrate computational simplicity and accuracy.
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.