LEADER 05253nam 2200625Ia 450 001 9910139753803321 005 20170926023557.0 010 $a1-282-27856-8 010 $a9786612278563 010 $a0-470-52216-X 010 $a0-470-52215-1 035 $a(CKB)1000000000790162 035 $a(EBL)456106 035 $a(OCoLC)441892546 035 $a(SSID)ssj0000354239 035 $a(PQKBManifestationID)11273853 035 $a(PQKBTitleCode)TC0000354239 035 $a(PQKBWorkID)10313200 035 $a(PQKB)11436665 035 $a(MiAaPQ)EBC456106 035 $a(EXLCZ)991000000000790162 100 $a20090223d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeneral linear methods for ordinary differential equations$b[electronic resource] /$fZdzislaw Jackiewicz 210 $aHoboken, N.Y. $cWiley$dc2009 215 $a1 online resource (500 p.) 300 $aDescription based upon print version of record. 311 $a0-470-40855-3 320 $aIncludes bibliographical references and index. 327 $aGeneral Linear Methods for Ordinary Differential Equations; CONTENTS; Preface; 1 Differential Equations and Systems; 1.1 The initial value problem; 1.2 Examples of differential equations and systems; 1.3 Existence and uniqueness of solutions; 1.4 Continuous dependence on initial values and the right-hand side; 1.5 Derivatives with respect to parameters and initial values; 1.6 Stability theory; 1.7 Stiff differential equations and systems; 1.8 Examples of stiff differential equations and systems; 2 Introduction to General Linear Methods; 2.1 Representation of general linear methods 327 $a2.2 Preconsistency, consistency, stage-consistency, and zero-stability2.3 Convergence; 2.4 Order and stage order conditions; 2.5 Local discretization error of methods of high stage order; 2.6 Linear stability theory of general linear methods; 2.7 Types of general linear methods; 2.8 Illustrative examples of general linear methods; 2.8.1 Type l: p = r = s = 2 and q = lor 2; 2.8.2 Type 2: p = r = s = 2 and q = 1 or 2; 2.8.3 Type 3: p = r = s = 2 and q = 1 or 2; 2.8.4 Type 4:p = r = s = 2 and q = 1 or 2; 2.9 Algebraic stability of general linear methods; 2.10 Underlying one-step method 327 $a2.11 Starting procedures2.12 Codes based on general linear methods; 3 Diagonally Implicit Multistage Integration Methods; 3.1 Representation of DIMSIMs; 3.2 Representation formulas for the coefficient matrix B; 3.3 A transformation for the analysis of DIMSIMs; 3.4 Construction of DIMSIMs of type 1; 3.5 Construction of DIMSIMs of type 2; 3.6 Construction of DIMSIMs of type 3; 3.7 Construction of DIMSIMs of type 4; 3.8 Fourier series approach to the construction of DIMSIMs of high order; 3.9 Least-squares minimization; 3.10 Examples of DIMSIMs of types 1 and 2 327 $a3.11 Nordsieck representation of DIMSIMs3.12 Representation formulas for coefficient matrices P and G·; 3.13 Examples of DIMSIMs in Nordsieck form; 3.14 Regularity properties of DIMSIMs; 4 Implementation of DIMSIMs; 4.1 Variable step size formulation of DIMSIMs; 4.2 Local error estimation; 4.3 Local error estimation for large step sizes; 4.4 Construction of continuous interpolants; 4.5 Step size and order changing strategy; 4.6 Updating the vector of external approximations; 4.7 Step-control stability of DIMSIMs; 4.8 Simplified Newton iterations for implicit methods 327 $a4.9 Numerical experiments with type 1 DIMSIMs4.10 Numerical experiments with type 2 DIMSIMs; 5 Two-Step Runge-Kutta Methods; 5.1 Representation of two-step Runge-Kutta methods; 5.2 Order conditions for TSRK methods; 5.3 Derivation of order conditions up to order 6; 5.4 Analysis of TSRK methods with one stage; 5.4.1 Explicit TSRK methods: s = l, p = 2 or 3; 5.4.2 Implicit TSRK methods: s = l, p = 2 or 3; 5.5 Analysis of TSRK methods with two stages; 5.5.1 Explicit TSRK methods: s = 2, p = 2, q = 1 or 2; 5.5.2 Implicit TSRK methods: s = 2, p = 2, q = 1 or 2 327 $a5.5.3 Explicit TSRK methods: s = 2, p = 4 or 5 330 $aLearn to develop numerical methods for ordinary differential equations General Linear Methods for Ordinary Differential Equations fills a gap in the existing literature by presenting a comprehensive and up-to-date collection of recent advances and developments in the field. This book provides modern coverage of the theory, construction, and implementation of both classical and modern general linear methods for solving ordinary differential equations as they apply to a variety of related areas, including mathematics, applied science, and engineering. The author provides the theoretical foun 606 $aDifferential equations, Linear 606 $aLinear systems 608 $aElectronic books. 615 0$aDifferential equations, Linear. 615 0$aLinear systems. 676 $a515 676 $a515.352 700 $aJackiewicz$b Zdzis?aw$f1950-$0874053 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139753803321 996 $aGeneral linear methods for ordinary differential equations$91951517 997 $aUNINA