Nyström methods for Fredholm integral equations using equispaced points

Theoretical analysis of Sinc-Nyström methods for Volterra integral equations

SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...

Lattice-Nyström method for Fredholm integral equations of the second kind with convolution type kernels

We consider Fredholm integral equations of the second kind of the form f(x) = g(x)+ ∫ k(x−y)f(y) dy, where g and k are given functions from weighted Korobov spaces. These spaces are characterized by a smoothness parameter α > 1 and weights γ1 ≥ γ2 ≥ · · · . The weight γj moderates the behavior of the functions with respect to the jth variable. We approximate f by the Nyström method using n rank...

Time-stepping methods for Volterra-Fredholm integral equations

The semidiscretization in space of Volterra-Fredholm integral equations (arising, for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive timestepping methods using certain DQ (= direct quadrature) methods which are employed in a way that exploits the local superconvergence properties of spatial colloca...

Approximate Solution of Linear Volterra-Fredholm Integral Equations and Systems of Volterra-Fredholm Integral Equations Using Taylor Expansion Method

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...