Bernoulli wavelet method for numerical solution of linear system of Fredholm integral equation of the second kind

• Published in: Alexandria engineering journal 2023-08, Vol.77, p.63-74
• Main Authors: Arafa, Heba M., Ramadan, Mohamed A.
• Format: Article
• Language: English
• Subjects: Accuracy; Bernoulli wavelet; Fredholm integral equations
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2023.06.061

One of the key tools for many fields of applied mathematics is the integral equations. Integral equations are widely utilized in many models, atmosphere–ocean dynamics, fluid mechanics, mathematical physics, and many other physical and engineering disciplines. A new numerical strategy based on the Bernoulli wavelet is introduced to solve system of Fredholm integral equations of second kind. In this paper, the Bernoulli wavelets are first built. Second, the system of Fredholm integral equations has been reduced into an algebraic system. In order to demonstrate the viability, and accuracy of the suggested Bernoulli wavelet approach, some numerical examples are offered at the end. The derived numerical results are examined with those from other numerical techniques and with exact solutions, demonstrating the superiority of the proposed method over those techniques. The novelty of proposed technique is that it can be extended for the numerical solution of two dimensional integral equations and differential equations appearing in engineering models, however some modifications will be required.