Two numerical treatments for solving the linear integro-differential Fredholm equation with a weakly singular kernel




Singular integral equations, Integro-differential equation, Fredholm equations


We compare the error behavior of two methods used to find a numerical solution of the linear integro-differential Fredholm equation with a weakly singular kernel in Banach space \(C^1[a,b]\). We construct an approximation solution based on the modified cubic b-spline collocation method. Another estimation of the exact solution, constructed by applying the numerical process of product and quadrature integration, is considered as well. Two proposed methods lead to solving a linear algebraic system. The stability and convergence of the cubic b-spline collocation estimate is proved. We test these methods on the concrete examples and compare the numerical results with the exact solution to show the efficiency and simplicity of the modified collocation method.

Author Biographies

Boutheina Tair

University 08 May 1945
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
Guelma, Algeria
• Leading Scientist

Sami Segni

University 08 May 1945
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
Guelma, Algeria
• Leading Scientist

Hamza Guebbai

University 08 May 1945
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
Guelma, Algeria
• Professor, Leading Researcher

Mourad Ghait

University 08 May 1945
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
Guelma, Algeria
• Leading Researcher


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How to Cite

Tair B., Segni S., Guebbai H., Ghait M. Two Numerical Treatments for Solving the Linear Integro-Differential Fredholm Equation With a Weakly Singular Kernel // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2022. 23. 117-136. doi 10.26089/NumMet.v23r208



Methods and algorithms of computational mathematics and their applications