On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained

Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces

A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −2()/2+sign()()=(), (0≤≤1), ()/+sign()()=(), (−1≤≤0), (0+)=(0−),(0+)=(0−),and(1)=(−1)+ for differential equations in a Hilbert space with a self-adjoint positive definite operator A is considered. The well-posedness of this difference scheme in Hölder spaces without a weight is established. Moreover, as applications, coercivity estimates in Hölder norms for the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained

On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem −d2u(t)/dt2+Au(t)=g(t), (0≤t≤1), du(t)/dt−Au(t)=f(t), (−1≤t≤0), u(1)=u(−1)+μ for differential equations in a Hilbert space H with a self-adjoint positive definite operator A is considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented