An integro-differential equation involving a convolution integral with a weakly singular kernel is considered. The kernel can be that of a fractional integral. The integro-differential equation is discretized using the discontinuous Galerkin method with piecewise constant basis functions. Sparse quadrature is introduced for the convolution term to overcome the problem with the growing amount of...

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast m...

A nonlinear integro-differential equation of convolution type with order of nonlinearity more than one and a stable trivial solution is considered. The integral in this equation has an exponential kernel and polynomial integrand. The difference analogue of the equation considered is constructed in the form of a difference equation with continuous time and it is shown that this difference analog...

An integro-differential equation on a tree graph is used to model the time evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an advection-diffusion process with coefficients that are constant on the edges of the graph. Appropriate boundary conditions are imposed at the outlet and u...

In this paper, a  fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.Error ana...

Describing turbulence and microinstabilities in fusion devices is often modelled with the gyrokinetic equation. During the time evolution of the distribution function a field equation for the electrostatic potential needs to be solved. In the case of adiabatic electrons it contains a fluxsurface-average term resulting in an integro-differential equation. Its numerical solution is time and memor...

1Department of Mathematics, Alzahra University, Tehran, Iran 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, Iran (Received November07, 2011, accepted March 1, 2012) Abstract. The sinc-collocation method is presented for solving second-order boundary value problems of nonlinear integro-differential equation. The method is effective...

This paper is about the design of a Sliding Mode Controller (SMC), with modified PI-D sliding surface, for the control of First Order Plus Dead Time (FOPDT) process. In the modified PI-D sliding surface, error is connected to the proportional and integral elements of the controller, and the derivative of the system output is connected to derivative element of the controller. The usage of PI-D s...

In this paper, we prove the existence and uniqueness of squaremean asymptotically almost automorphic mild solution of a class of partial nonlocal neutral stochastic functional integro-differential equations with resolvent operators in a real separable Hilbert space. An example illustrating our main result is given.