Analytical and Numerical Solutions of Linear Volterra Integral Equations of the Second Kind with Weakly Singular Kernel by using the Sixth Order of Non_polynomial Spline Functions by Matlab

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ELGAILI ABDALLAH ELHASSAN IBRAHIM , Abdel Radi Abdel Rahman Abdel GadirAbdel Rahman , Zakieldeen Aboabuda Mohamed Alhassn Ali, Reem Hussain Ibrahim Hassan

Abstract

Volterra Integral Equations has wide range of the applications in physics and
engineering problems.Spline function can be integrated and differentiated due to being piece
wise polynomials and can easily store and implemented on digital computers, nonpolynomial
spline function apiece wise is a blend of trigonometric, as well as ,polynomial
basis function ,which form a complete extended Chebyshev space.Matlab is a high-level
software package with many built in functions that make the learning of numerical methods
much easier and interesting.The aims of this paper is to focus and use the sixth order nonpolynomial
spline functions to solve linear Voltera integral equations with Weakly Singular
Kernel. We followed the applied numerical method using Matlab .Numerical examples are
presented to illustrate the applications of this method and to compare the computed results
with other numerical methods for exact solutions.

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