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Finite-difference methods (FDM) are a class of numerical techniques which are used for solving differential equations by estimating derivatives with finite differences. It involves discretizing the spatial domain and time interval. The value of the solution at these discrete points is approximated by solving algebraic equations having finite differences and values from adjacent points. Finite difference methods transform ordinary differential equations or partial differential equations, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently, which has led to the widespread use of FDM in modern numerical analysis. It is considered to be one of the most common approaches to the numerical solution of partial differential equations. This book is compiled in such a manner, that it will provide in-depth knowledge about the theory and practice of finite difference computing. Also included herein is a detailed explanation of the various concepts and applications of this method. Students, researchers, experts and all associated with finite-difference methods will benefit alike from this book.
