Finite difference and finite volume methods for elliptic equations (Q2701772)

Basic mathematical and algorithmic principles of the finite difference and finite volume methods for elliptic equations are presented. Discretization algorithms are described for mixed boundary problems in complicated domains. Basic theoretical problems of approximation, stability, convergence, and error estimation are studied. Higher order compact difference schemes for differential equations with variable coefficients are investigated. Methods for constructing balance approximations of various orders on triangular or quadrangular finite volumes are presented. Modern computational technologies are considered based on mesh generation and structural, spectral, and monotonicity properties of algebraic equations. Effective direct and iterative methods for high order systems with sparse matrices are studied.NEWLINENEWLINEThe book is aimed at post graduate students and specialists in computational and applied mathematics.