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<p><b>Examines numerical and semi&#45;analytical methods for differential equations that can be used for solving practical ODEs and PDEs</b> <p>This student&#45;friendly book deals with various approaches for solving differential equations numerically or semi&#45;analytically depending on the type of equations and offers simple example problems to help readers along. <p>Featuring both traditional and recent methods, <i>Advanced Numerical and Semi&#45;Analytical Methods for Differential Equations</i> 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 &#40;BCOPs&#41; is introduced next. The book then discusses Finite Difference Method &#40;FDM&#41;, Finite Element Method &#40;FEM&#41;, Finite Volume Method &#40;FVM&#41;, and Boundary Element Method &#40;BEM&#41;. Following that, analytical/semi<i>&#45;</i>analytic methods like Akbari Ganji&#39;s Method &#40;AGM&#41; and Exp&#45;function are used to solve nonlinear differential equations. Nonlinear differential equations using semi&#45;analytical methods are also addressed, namely Adomian Decomposition Method &#40;ADM&#41;, Homotopy Perturbation Method &#40;HPM&#41;, Variational Iteration Method &#40;VIM&#41;, and Homotopy Analysis Method &#40;HAM&#41;. 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: <ul> <li>Discusses various methods for solving linear and nonlinear ODEs and PDEs</li> <li>Covers basic numerical techniques for solving differential equations along with various discretization methods</li> <li>Investigates nonlinear differential equations using semi&#45;analytical methods</li> <li>Examines differential equations in an uncertain environment</li> <li>Includes a new scenario in which uncertainty &#40;in term of intervals and fuzzy numbers&#41; has been included in differential equations</li> <li>Contains solved example problems, as well as some unsolved problems for self&#45;validation of the topics covered</li> </ul> <p><i>Advanced Numerical and Semi&#45;Analytical Methods for Differential Equations</i> is an excellent textbook for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi&#45;analytically.

Brings mathematics to bear on your real-world, scientific problemsMathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics.The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include:Structural static and vibration problemsHeat conduction and diffusion problemsFluid dynamics problemsThe book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: * Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems * Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications * Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications * Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science.