Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation | Zendy

K. R. Raslan | Zendy; Khalid K. Ali | Zendy; Reda Gamal Ahmed | Zendy; Hind K. Al-Jeaid | Zendy; Amira AbdElall Ibrahim | Zendy

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Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation

Author(s) -

K. R. Raslan,

Khalid K. Ali,

Reda Gamal Ahmed,

Hind K. Al-Jeaid,

Amira AbdElall Ibrahim

Publication year - 2022

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2022/4773005

Subject(s) - mathematics , boundary value problem , uniqueness , volterra integral equation , fredholm integral equation , mathematical analysis , volterra equations , fredholm theory , algebraic equation , differential equation , integro differential equation , integral equation , initial value problem , nonlinear system , physics , first order partial differential equation , quantum mechanics

In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method.

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