The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

In this paper, the solution of a moving Volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. These equations, which are classified as, Cauchy singular equations, ...

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...

Existence of positive solutions for singular impulsive differential equations with integral boundary conditions on an infinite interval in Banach spaces∗ Xu Chen, Xingqiu Zhang1,2† 1 School of Mathematics, Liaocheng University, Liaocheng, 252059, Shandong, China 2 School of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China Email: [email protected], zhxq19750...

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction-diffusion equations with spatially periodic diffusive fluxes. The result connects wave pinning phenomena in lattice differential equations and in reaction-diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, wher...