Nonlinear Analysis Modelling and Control · 2014 · 21 citations · 30 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisDifference EquationsIterative SolversNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsDifference OperatorsEigenvaluesElliptic Partial Differential EquationsSpectral Convergence
The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented. 1The research was partially supported by the Research Council of Lithuania (grant No. MIP-051/2011). 2The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).
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THE THEORY OF DIFFERENCE SCHEMES
I.M. KHABAZA · Journal of the London Mathematical Society · 1967 · 1K citations