In this paper, we investigate the numerical study of nonlinear Fredholm integro-differential equation with fractional Caputo-Fabrizio derivative. We use Hermite wavelets and collocation technique to approximate exact solution by reducing a algebraic system. Furthermore, apply method on certain examples check its accuracy validity.

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For continuous entropy analysis to hold and ensure Galilean invariance in technique, system requires use of non-conservat...

Dynamical response of nanomechanical cantilever structures immersed in a viscous fluid is important to in vitro single-molecule force spectroscopy, biomolecular recognition of disease-specific proteins, and the study of microscopic protein dynamics. Here we study the stochastic response of biofunctionalized nanomechanical cantilever beams in a viscous fluid. Using the fluctuation-dissipation th...

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orth...

For variation-aware capacitance extraction, stochastic collocation method (SCM) based on Homogeneous Chaos expansion has the exponential convergence rate for Gaussian geometric variations, and is considered as the optimal solution using a quadratic model to model the parasitic capacitances. However, when geometric variations are measured from the real test chip, they are not necessarily Gaussia...

The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators from which we propose to extract a small number of relevant and independent deformations by using a truncated Karhunen–Loève expansion. The ra...