Stability of difference schemes for two-dimensional parabolic equations with non-local boundary conditions

• Published in: Applied mathematics and computation Vol. 215; no. 7; pp. 2716 - 2732
• Main Authors: Ivanauskas, F., Meškauskas, T., Sapagovas, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2009; Elsevier
• Subjects: Algebra; Algebraic geometry; Exact sciences and technology; Finite difference schemes; Mathematical analysis; Mathematics; Non-local boundary conditions; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Operator theory; Parabolic equations; Sciences and techniques of general use; Stepwise stability; Non-local boundary conditions; Parabolic equations; Finite difference schemes; Stepwise stability; Transcendental equation; Difference scheme; Eigenvector; Numerical linear algebra; Eigenvalue; Iterative method; Boundary condition; Equation system; Non linear equation; Direct method; Two dimensional equation; Parabolic equation; Numerical analysis; Linear system; Linear equation; Matrix inversion; Applied mathematics; Algebraic equation; Numerical stability; Finite difference method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.09.012

The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze–Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied. Depending on the values of parameters in non-local conditions, this matrix can have one zero, one negative or complex eigenvalues. The stepwise stability is proved and the domain of stability of difference schemes is found.