LEADER 04131nam 22006255 450 001 9910254074803321 005 20200703231532.0 010 $a81-322-2812-X 024 7 $a10.1007/978-81-322-2812-7 035 $a(CKB)3710000000717752 035 $a(DE-He213)978-81-322-2812-7 035 $a(MiAaPQ)EBC5588937 035 $a(MiAaPQ)EBC6314773 035 $a(Au-PeEL)EBL5588937 035 $a(OCoLC)950320282 035 $a(Au-PeEL)EBL6314773 035 $a(PPN)194079589 035 $a(EXLCZ)993710000000717752 100 $a20160509d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonlinear Ordinary Differential Equations$b[electronic resource] $eAnalytical Approximation and Numerical Methods /$fby Martin Hermann, Masoud Saravi 205 $a1st ed. 2016. 210 1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2016. 215 $a1 online resource (XVI, 310 p. 53 illus.) 311 $a81-322-2810-3 327 $aA 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. 330 $aThe 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. 606 $aDifferential equations 606 $aNumerical analysis 606 $aMathematical physics 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aDifferential equations. 615 0$aNumerical analysis. 615 0$aMathematical physics. 615 14$aOrdinary Differential Equations. 615 24$aNumerical Analysis. 615 24$aMathematical Physics. 615 24$aMathematical Applications in the Physical Sciences. 676 $a515.352 700 $aHermann$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721182 702 $aSaravi$b Masoud$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254074803321 996 $aNonlinear Ordinary Differential Equations$91906805 997 $aUNINA