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Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics) J.W. Thomas
Publisher: Springer

Written in a clear, accessible style, the third edition incorporates three software packages--Maple®, Excel®, and MATLAB®--in problems and examples throughout the text. Numerical Methods for Engineers and Scientists. Oxford Applied Mathematics & Computing Science Series. The ADI (alternate directions implicit) method is widely used for the numerical solution of multidimensional parabolic PDE (partial differential equations). Numerical Solution of Partial Differential Equations: Finite Difference Methods. \begin{array}{lll} B^2 - 4AC < 0 & \text{Elliptic} & \text{Complex characteristic curves} \\ B^2 - 4AC = 0 & \text{Parabolic} & \text{Real and repeated characteristic curves}\\ B^2 - 4AC > 0 & \text{Hyperbolic} & \text{Real and distinct characteristic curves} Hoffman, J. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. This third edition of Advanced throughout the text. To the best of the author's knowledge, what has not been studied is the effects of a surface singularity to a PDE with geometric coefficients living on the surface. Mathematics Institute The CH equation brings several numerical difficulties: it is a fourth order parabolic equation with a non-linear term and it evolves with very different time scales. In particular, we discuss the algorithmic and computer The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. Topics covered include series methods, Laplace transforms, matrix theory and applications, vector analysis, Fourier series and transforms, partial differential equations, numerical methods using finite differences, complex variables, and wavelets. Furthermore, in order to fully capture the To solve this problem numerically a semi-smooth Newton method is applied.