On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions

Abstract

Abstract. We consider the stability of a weighted finite difference scheme for a linear hyperbolic equation with nonlocal integral boundary condition. By studying the spectrum of the transition matrix of the three-layered difference scheme we obtain a sufficient stability condition in a special matrix norm.

Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition

“…Based on Property 5, it is possible to assert that 1. Iterative method (20) of Theorem 3 converges asymptotically slower than method (16) of Theorem 1 as well as than method (18) of Theorem 2; 2. Iterative method (17) converges asymptotically slower than method (16), and method (21) slower than method (20).…”

“…Conclusion 2. If 0 γ < γ 0 and hypothesis (H2) is true, then iterative methods (16), (17), (18), (20) and (21) for system (4)-(6) expressed by form (12) converge. Conclusion 1 is valid for these iterative methods.…”

“…The results of the spectrum structure analysis have been applied to investigate the convergence of iterative methods for elliptic equations [24,29,30] as well as stability of difference schemes for parabolic [11,12,14,16,27] and hyperbolic equations [15,20].…”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…The spectrum and eigenfunctions for SLP (49), (51)- (52) were investigated for all values of parameters γ 1 and γ 2 in [143]. For this problem: 1) all eigenvalues are simple and real; 2) if γ < 2, then λ ∈ (0, 4/h 2 ];…”

“…Novickij and Štikonas consider the stability of a weighted FDS for a linear hyperbolic equation with integral NBCs [143].…”