The iterated Galerkin method for linear integro-differential equations
Journal of Computational and Applied Mathematics
Wavelet-Galerkin method for integro-differential equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
Fixed point method for solving nonlinear quadratic Volterra integral equations
Computers & Mathematics with Applications
Wavelet Collocation Method and Multilevel Augmentation Method for Hammerstein Equations
SIAM Journal on Scientific Computing
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In this paper, we present an existence of solution for a functional integro-differential equation with an integral boundary condition arising in chemical engineering, underground water flow and population dynamics, and other field of physics and mathematical chemistry. By using the techniques of noncompactness measures, we employ the basic fixed point theorems such as Darbo's theorem to obtain the mentioned aim in Banach algebra. Then this paper presents a powerful numerical approach based on Sinc approximation to solve the equation. Then convergence of this technique is discussed by preparing a theorem which shows exponential type convergence rate and guarantees the applicability of that. Finally, some numerical examples are given to confirm efficiency and accuracy of the numerical scheme.