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Zbl 1175.65103
Ashyralyev, Allaberen; Ozdemir, Yildirim
On stable implicit difference scheme for hyperbolic-parabolic equations in a Hilbert space. (English)
[J] Numer. Methods Partial Differ. Equations 25, No. 5, 1100-1118 (2009). ISSN 0749-159X; ISSN 1098-2426/e

For a self-adjoint, positive-definite operator $A$ the authors consider the differential equation $u' + Au = g$ for $-1 < t < 0$ followed by $u'' + Au = f$ for $0 < t < 1$. The initial condition at $t = -1$ depends linearly on future values of $u$ for $0 < t < 1$. The authors analyze the stability of an implicit discretization.
[Gerald W. Hedstrom (Pleasanton)]

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
35M13
34G10 Linear ODE in abstract spaces
65L12 Finite difference methods for ODE
65L20 Stability of numerical methods for ODE
65J08

Keywords: hyperbolic-parabolic equation; nonlocal boundary-value problem; implicit difference scheme; Hilbert space; stability

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Zentralblatt MATH Berlin [Germany]