Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...

We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be det...

We propose a new class of mapping-based nonlinear quadratic Volterra filters for image enhancement. The input signal is mapped prior to filtering by a memoryless one-to-one nonlinear mapping function. The mapping function can be described by any arbitrary function and implemented by a simple look-up table. If necessary, an inverse mapping function is applied after filtering. Using this general ...

Over the last decade, the field of geometric integration has rapidly established itself as one of the core research areas in numerical ordinary differential equations. Geometric integrators are numerical methods which preserve some of the mathematical or physical properties of the system they are approximating. In the case of the Lotka-Volterra equations, which are a Poisson system, a good geom...

In this article, the numerical solution of mixed Volterra–Fredholm integro-differential equations multi-fractional order less than or equal to one in Caputo sense (V-FIFDEs) under initial conditions is presented with powerful algorithms. The method based upon quadrature rule aid finite difference approximation derivative usage collocation points. For treatments, our technique converts V-FIFDEs ...