Integral solutions to boundary quantum Knizhnik–Zamolodchikov equations

Twin solutions to semipositone boundary value problems for fractional differential equations with coupled integral boundary conditions

This paper investigates the existence of at least two positive solutions for the following high-order fractional semipositone boundary value problem (SBVP, for short) with coupled integral boundary value conditions:  D0+u(t) + λf(t,u(t), v(t)) = 0, t ∈ (0, 1), D0+v(t) + λg(t,u(t), v(t)) = 0, t ∈ (0, 1), u(j)(0) = v(j)(0) = 0, j = 0, 1, 2, · · · ,n− 2, Dα−1 0+ u(1) = λ1 ∫η1 0 v(t)...

Approximate Solutions to Three-Point Boundary Value Problems with Two-Space Integral Condition for Parabolic Equations

and Applied Analysis 3 The inner product of H Ω is defined by 〈u x, t , v x, t 〉H 1 ∑ j 0 [ 1 ∑ i 0 ∂ j i tjxi u 0, 0 ∂ i tjxi v 0, 0 ∫1 0 ∂ j 3 tjx3 u x, 0 ∂ 3 tjx3 v x, 0 dx ]

Exact solutions of nonlinear interval Volterra integral equations

Stokes-Darcy boundary integral solutions using preconditioners

In a system where a free fluid flow is coupled to flow in a porous medium, different PDEs are solved simultaneously in two subdomains. We consider steady Stokes equations in the free region, coupled across a fixed interface to Darcy equations in the porous substrate. In this paper, the numerical solution is obtained using the boundary integral formulation with regularized Green’s function. High...

The Numerical Solution of Boundary Integral Equations

Much of the research on the numerical analysis of Fredholm type integral equations during the past ten years has centered on the solution of boundary integral equations (BIE). A great deal of this research has been on the numerical solution of BIE on simple closed boundary curves S for planar regions. When a BIE is de ned on a smooth curve S, there are many numerical methods for solving the equ...