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Informationen zum Autor SNEHASHISH CHAKRAVERTY, PHD, is Professor in the Department of Mathematics at National Institute of Technology, Rourkela, Odisha, India. He is also the author of Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications and 12 other books . NISHA RANI MAHATO is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where she is pursuing her PhD. PERUMANDLA KARUNAKAR is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where he is pursuing his PhD. THARASI DILLESWAR RAO, is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology, Rourkela, Odisha, India where he is pursuing his PhD. Klappentext Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi-Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi - analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi-Analytical Methods for Differential Equations is an excellent textbook for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically. Inhaltsverzeichnis Acknowledgments xi Preface xiii 1 Basic Numerical Methods 1 1.1 Introduction 1 1.2 Ordinary Differential Equation 2 1.3 Euler Method 2 1.4 Improved Euler Method 5 1.5 Runge-Kutta Methods 7 1.5.1 Midpoint Method 7 1.5.2 Runge-Kutta Fourth Order 8 1.6 Multistep Methods 10 1.6.1 Adams-Bashforth Method 10 1.6.2 Adams-Moulton Method 10 1.7 Higher-Order ODE 13 References 16 2 Integral Transforms
