Solution of systems of integro-differential equations using numerical treatment of fixed point

Numerical solving of several types of two‐dimensional integral equations and estimation of error bound

“…Let q and G be C 1 -functions, such that G, G s , G t , G x , G , and G u satisfy a global Lipschitz condition in the third variable. Let b 0 (s, t) ∶=ũ(s, t) ∈ C 1 (Ω) and define inductively as in (30) the function I r−1 . Then,…”

“…The numerical method used to solve the above equations is based on 2 analytical techniques: the Banach fixed‐point theorem and Faber‐Schauder systems in a Banach space. Such tools have been used successfully in the study of certain types of 1‐dimensional integral and integro‐differential equations . The 2‐dimensional linear Volterra integral equation has been studied using geometric series theorem and Schauder bases in a Banach space …”

“…Such tools have been used successfully in the study of certain types of 1-dimensional integral and integro-differential equations. [28][29][30] The 2-dimensional linear Volterra integral equation has been studied using geometric series theorem and Schauder bases in a Banach space. 31 Math Meth Appl Sci.…”

Solving Fuzzy System of Volterra Integro-differential Equations by using Adomian Decomposition Method

“…Hassan and Peter [16] solve new iterative method with a reliable algorithm and applied to the systems of Volterra integro-differential equations. Berenguer et al [17] have been solved systems of integrodifferential equations using numerical of fixed Point. Biazar and Aminikhah [18] have been used Variational iteration method (VIM) for solving nonlinear integral-differential equations.…”

Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

“…The exact solutions of these systems are difficult to find. In finding the approximate solutions, different approaches in the literature have been used such as homotopy perturbation method (HPM), 1 homotopy analysis method (HAM), 2 differential transformation method (DTM), 3 Genocchi polynomials (GP), 4 reproducing kernel Hilbert space method (RKHSM), 5 Chebyshev wavelets method (CWM), 6 fixed point method (FPM), 7 Sinc-collocation method (SCM), 8 Haar functions method (HFM), 9 Adomian decomposition method (ADM), 10 and relaxed Monte Carlo method (RMCM). 11 In the present attempt, optimal homotopy asymptotic method (OHAM) is used, which was introduced by Marinca et al 12,13 for the solution of differential equations.…”