Abstract
ABSTRACTIn this study, a collocation method, one of the type of projection methods based on the generalized Bernstein polynomials, is developed for the solution of high-order linear Fredholm–Volterra integro-differential equations containing derivatives of unknown function in the integral part. The method is valid for the mixed conditions. The convergence analysis and error bounds of the method are also given. Besides, six examples are presented to demonstrate the applicability and validity of the method.
Highlights
In the early 1900s, Vito Volterra has introduced new type of equations called as integro-differential equations for his research study on population growth phenomenon
Since it is not usually possible to find an exact solution of the integrodifferential equations, new trends on the numerical methods for solving these types of equations have been developed with calculating techniques and programming supports
One of the most frequently used numerical method is collocation method. Collocation methods such as Bessel [1], Chebyshev [2,3], Taylor polynomials [4] and B-spline functions [5] have been given for approximating the solutions of linear Fredholm–Volterra integro-differential equations
Summary
In the early 1900s, Vito Volterra has introduced new type of equations called as integro-differential equations for his research study on population growth phenomenon. Collocation methods such as Bessel [1], Chebyshev [2,3], Taylor polynomials [4] and B-spline functions [5] have been given for approximating the solutions of linear Fredholm–Volterra integro-differential equations. By benefiting from the definition of the generalized Bernstein polynomials and their approach [6] we develop a collocation method for approximating the solution of mth-order linear Fredholm–Volterra integro-differential equation in the most general form as m bq ak (x) y(k)(x) = g (x) + λ1 fk (x, t) y(k)(t) dt k=0 a k=0 xr. Let’s give the following Theorem 1.1 (see [8]) that is an important relation between the generalized Bernstein basis polynomials and their derivatives. Some numerical examples are given to demonstrate the efficiency of the method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
