Linear Volterra integro-differential equation and Schauder bases

High-order nonlinear initial-value problems countably determined

“…It is possible to consider any Schauder basis in the space C [α, α + β], although we have chosen this particular basis for the sake of simplicity. Let us also point out that Schauder bases have been used as a fundamental tool in order to solve numerically some other integral, differential, and integro-differential equations (see [1][2][3] …”

An Iterative Scheme for Solving Systems of Nonlinear Fredholm Integrodifferential Equations

“…Proof. The announced estimation follows from the inequalities obtained in Propositions 4 and 5 in [11], respectively, and applying Theorem 1.…”

“…Zarebnia and Ali Abadi [10] use the Sinc-collocation method to solve systems of nonlinear second-order integrodifferential equations. Berenguer et al used in [11][12][13][14] von Neumann series, fixed-point techniques, and Faber-Schauder systems in Banach spaces to solve integro and integrodifferential equations.…”

Numerical solving initial value problem for Fredholm type linear integro-differential equation system

“…However, the necessary and sufficient for a unique solution for Eqs. (1.1) and (1.2) could be found in [1,8,11,14,20,21,23]. …”