04131nam 22006255 450 991025407480332120200703231532.081-322-2812-X10.1007/978-81-322-2812-7(CKB)3710000000717752(DE-He213)978-81-322-2812-7(MiAaPQ)EBC5588937(MiAaPQ)EBC6314773(Au-PeEL)EBL5588937(OCoLC)950320282(Au-PeEL)EBL6314773(PPN)194079589(EXLCZ)99371000000071775220160509d2016 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierNonlinear Ordinary Differential Equations[electronic resource] Analytical Approximation and Numerical Methods /by Martin Hermann, Masoud Saravi1st ed. 2016.New Delhi :Springer India :Imprint: Springer,2016.1 online resource (XVI, 310 p. 53 illus.) 81-322-2810-3 A Brief Review of Elementary Analytical Methods for Solving Nonlinear ODEs -- Analytical Approximation Methods -- Further Analytical Approximation Methods and Some Applications -- Nonlinear Two-Point Boundary Value Problems -- Numerical Treatment of Parameterized Two-Point Boundary Value Problems.The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.Differential equationsNumerical analysisMathematical physicsOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Differential equations.Numerical analysis.Mathematical physics.Ordinary Differential Equations.Numerical Analysis.Mathematical Physics.Mathematical Applications in the Physical Sciences.515.352Hermann Martinauthttp://id.loc.gov/vocabulary/relators/aut721182Saravi Masoudauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254074803321Nonlinear Ordinary Differential Equations1906805UNINA