Advanced numerical and semi analytical methods for differential equations:
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 si...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, NJ
John Wiley & Sons, Inc.
2019
|
| Schlagwörter: | |
| Links: | https://learning.oreilly.com/library/view/-/9781119423423/?ar |
| Zusammenfassung: | 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 text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically. |
| Beschreibung: | Includes index. - Includes bibliographical references and index. - Description based on print version record and CIP data provided by publisher |
| Umfang: | 1 Online-Ressource |
| ISBN: | 9781119423447 1119423449 9781119423430 1119423430 9781119423461 1119423465 |
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| spelling | Advanced numerical and semi analytical methods for differential equations Snehashish Chakraverty (National Institute of Technology Rourkela, Odisha, India) [and three others] Hoboken, NJ John Wiley & Sons, Inc. 2019 1 Online-Ressource Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Includes index. - Includes bibliographical references and index. - Description based on print version record and CIP data provided by publisher 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 text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically. Differential equations Numerical solutions Équations différentielles ; Solutions numériques MATHEMATICS ; Calculus MATHEMATICS ; Mathematical Analysis Differential equations Chakraverty, Snehashish VerfasserIn aut 9781119423423 Erscheint auch als Druck-Ausgabe 9781119423423 |
| spellingShingle | Chakraverty, Snehashish Advanced numerical and semi analytical methods for differential equations Differential equations Numerical solutions Équations différentielles ; Solutions numériques MATHEMATICS ; Calculus MATHEMATICS ; Mathematical Analysis Differential equations |
| title | Advanced numerical and semi analytical methods for differential equations |
| title_auth | Advanced numerical and semi analytical methods for differential equations |
| title_exact_search | Advanced numerical and semi analytical methods for differential equations |
| title_full | Advanced numerical and semi analytical methods for differential equations Snehashish Chakraverty (National Institute of Technology Rourkela, Odisha, India) [and three others] |
| title_fullStr | Advanced numerical and semi analytical methods for differential equations Snehashish Chakraverty (National Institute of Technology Rourkela, Odisha, India) [and three others] |
| title_full_unstemmed | Advanced numerical and semi analytical methods for differential equations Snehashish Chakraverty (National Institute of Technology Rourkela, Odisha, India) [and three others] |
| title_short | Advanced numerical and semi analytical methods for differential equations |
| title_sort | advanced numerical and semi analytical methods for differential equations |
| topic | Differential equations Numerical solutions Équations différentielles ; Solutions numériques MATHEMATICS ; Calculus MATHEMATICS ; Mathematical Analysis Differential equations |
| topic_facet | Differential equations Numerical solutions Équations différentielles ; Solutions numériques MATHEMATICS ; Calculus MATHEMATICS ; Mathematical Analysis Differential equations |
| work_keys_str_mv | AT chakravertysnehashish advancednumericalandsemianalyticalmethodsfordifferentialequations |