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Analysis of Finite Difference Schemes - For Linear Partial Differential Equations with Generalized Solutions (Paperback, Softcover reprint of the original 1st ed. 2014)
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Analysis of Finite Difference Schemes - For Linear Partial Differential Equations with Generalized Solutions (Paperback, Softcover reprint of the original 1st ed. 2014)
Series: Springer Series in Computational Mathematics, 46
Expected to ship within 10 - 15 working days
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This book develops a systematic and rigorous mathematical theory of
finite difference methods for linear elliptic, parabolic and
hyperbolic partial differential equations with nonsmooth solutions.
Finite difference methods are a classical class of techniques for
the numerical approximation of partial differential equations.
Traditionally, their convergence analysis presupposes the
smoothness of the coefficients, source terms, initial and boundary
data, and of the associated solution to the differential equation.
This then enables the application of elementary analytical tools to
explore their stability and accuracy. The assumptions on the
smoothness of the data and of the associated analytical solution
are however frequently unrealistic. There is a wealth of boundary -
and initial - value problems, arising from various applications in
physics and engineering, where the data and the corresponding
solution exhibit lack of regularity. In such instances classical
techniques for the error analysis of finite difference schemes
break down. The objective of this book is to develop the
mathematical theory of finite difference schemes for linear partial
differential equations with nonsmooth solutions. Analysis of Finite
Difference Schemes is aimed at researchers and graduate students
interested in the mathematical theory of numerical methods for the
approximate solution of partial differential equations.
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