Toeplitz Matrix and Nyström Method for Solving Linear Fractional Integro-differential Equation
Keywords:Systems of linear singular integral equations, Integro-partial differential equations, Picard method, Toeplitz matrix, Nyström method
In this paper, the Volterra-Fredholm integral equation is derived from a linear integro-differential equation with a fractional order 0 < α < 1 using Riemann–Liouville fractional integral. The existence and uniqueness of the solution are proved using the Picard method. Popular numerical methods; the Toeplitz matrix, and the product Nystr ̈om are used in the solution. These methods will prove their effective in solving this type of equation. Two examples are solved using the mentioned methods and the estimation error is calculated. Finally, a comparison between the numerical results is made.
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