A numerical treatment of the delayed Ambartsumian equation over large interval

Abstract

In this paper, a numerical technique based on matrix collocation method is presented for approximating the solution of the Ambartsumian equation in terms of the shifted Bernoulli polynomials. Shifted Bernoulli operational matrix of differentiation is first derived and then utilized to reduce the problem into a system of linear algebraic equations which can be solved to find the solution. Results are included to demonstrate the validity and applicability of the technique and compared with other methods. These results show the efficiency and accuracy of the presented algorithm and also the physical behaviour of the presented problem over large intervals.

Subject Classification:

• 85A04
• 65N35

Keywords:

• Shifted Bernoulli
• Ambartsumian equation
• Astrophysics
• Numerical solution