In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are des...

An algorithm for parallel processing the discrete nonlinear system for solving Fredholm integro-differential equations with twopoint boundary conditions on a PC cluster is considered. The cost of calculating the history terms is expensive and improvements are motivated by considering different architectures. The algorithm has been modified to minimize the communication overhead inherent in a di...

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prov...

For scientists conducting research, fractional integral differential equation analysis is crucial. Therefore, in this study, we investigate utilizing a novel method called the decomposition method, which applicable to nonlinear Fredholm integro-differential equations. Then, apply approach five test problems for general derivative [Formula: see text] involving To best of our knowledge, are first...

Abstract In this paper, a nonclassical sinc collocation method is constructed for the numerical solution of systems second-order integro-differential equations Volterra and Fredholm types. The novelty approach based on using new weight function instead classic ones. functions used to reduce system algebraic equations. Furthermore, convergence proposed theoretically, showing that converges expon...

This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate singular integral, unknown function approximated by an interpolation polynomial is rewritten as Taylor series expansion. A system linear FIDEs obtained using equally spaced points collocation solved obtai...

This study introduced new technique which is based on a combination of the least-squares (LST) with Chebyshev and Legendre polynomials for finding approximate solutions higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to mixed conditions. Two examples second third-order FVIDEs are considered illustrate proposed method, numerical results comprised demonstrate...

In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using equationwhich equivalent to set of algebraic the method transforms equation. When compared other methods that have been proposed in literature, numerical results from suggested technique reveal it effective and p...