LEADER 05501nam 2200661 450 001 9910678196103321 005 20170815154151.0 010 $a1-283-33249-3 010 $a9786613332493 010 $a1-118-16449-0 010 $a1-118-16452-0 035 $a(CKB)2670000000133352 035 $a(EBL)818504 035 $a(SSID)ssj0000555233 035 $a(PQKBManifestationID)11356221 035 $a(PQKBTitleCode)TC0000555233 035 $a(PQKBWorkID)10520272 035 $a(PQKB)10532505 035 $a(MiAaPQ)EBC818504 035 $a(PPN)169732908 035 $a(OCoLC)768243510 035 $a(EXLCZ)992670000000133352 100 $a20160818h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNumerical solution of ordinary differential equations /$fKendall E. Atkinson, Weimin Han, David Stewart 210 1$aHoboken, New Jersey :$cWiley,$d2009. 210 4$dİ2009 215 $a1 online resource (272 p.) 225 1 $aPure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and Tracts 300 $aDescription based upon print version of record. 311 $a0-470-04294-X 320 $aIncludes bibliographical references and index. 327 $aNumerical Solution of Ordinary Differential Equations; CONTENTS; Introduction; 1 Theory of differential equations: An introduction; 1.1 General solvability theory; 1.2 Stability of the initial value problem; 1.3 Direction fields; Problems; 2 Euler's method; 2.1 Definition of Euler's method; 2.2 Error analysis of Euler's method; 2.3 Asymptotic error analysis; 2.3.1 Richardson extrapolation; 2.4 Numerical stability; 2.4.1 Rounding error accumulation; Problems; 3 Systems of differential equations; 3.1 Higher-order differential equations; 3.2 Numerical methods for systems; Problems 327 $a4 The backward Euler method and the trapezoidal method4.1 The backward Euler method; 4.2 The trapezoidal method; Problems; 5 Taylor and Runge-Kutta methods; 5.1 Taylor methods; 5.2 Runge-Kutta methods; 5.2.1 A general framework for explicit Runge-Kutta methods; 5.3 Convergence, stability, and asymptotic error; 5.3.1 Error prediction and control; 5.4 Runge-Kutta-Fehlberg methods; 5.5 MATLAB codes; 5.6 Implicit Runge-Kutta methods; 5.6.1 Two-point collocation methods; Problems; 6 Multistep methods; 6.1 Adams-Bashforth methods; 6.2 Adams-Moulton methods; 6.3 Computer codes 327 $a6.3.1 MATLAB ODE codesProblems; 7 General error analysis for multistep methods; 7.1 Truncation error; 7.2 Convergence; 7.3 A general error analysis; 7.3.1 Stability theory; 7.3.2 Convergence theory; 7.3.3 Relative stability and weak stability; Problems; 8 Stiff differential equations; 8.1 The method of lines for a parabolic equation; 8.1.1 MATLAB programs for the method of lines; 8.2 Backward differentiation formulas; 8.3 Stability regions for multistep methods; 8.4 Additional sources of difficulty; 8.4.1 A-stability and L-stability; 8.4.2 Time-varying problems and stability 327 $a8.5 Solving the finite-difference method8.6 Computer codes; Problems; 9 Implicit RK methods for stiff differential equations; 9.1 Families of implicit Runge-Kutta methods; 9.2 Stability of Runge-Kutta methods; 9.3 Order reduction; 9.4 Runge-Kutta methods for stiff equations in practice; Problems; 10 Differential algebraic equations; 10.1 Initial conditions and drift; 10.2 DAEs as stiff differential equations; 10.3 Numerical issues: higher index problems; 10.4 Backward differentiation methods for DAEs; 10.4.1 Index 1 problems; 10.4.2 Index 2 problems; 10.5 Runge-Kutta methods for DAEs 327 $a10.5.1 Index 1 problems10.5.2 Index 2 problems; 10.6 Index three problems from mechanics; 10.6.1 Runge-Kutta methods for mechanical index 3 systems; 10.7 Higher index DAEs; Problems; 11 Two-point boundary value problems; 11.1 A finite-difference method; 11.1.1 Convergence; 11.1.2 A numerical example; 11.1.3 Boundary conditions involving the derivative; 11.2 Nonlinear two-point boundary value problems; 11.2.1 Finite difference methods; 11.2.2 Shooting methods; 11.2.3 Collocation methods; 11.2.4 Other methods and problems; Problems; 12 Volterra integral equations; 12.1 Solvability theory 327 $a12.1.1 Special equations 330 $aA concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in o 410 0$aInterscience tracts in pure and applied mathematics. 606 $aDifferential equations$xNumerical solutions 615 0$aDifferential equations$xNumerical solutions. 676 $a515.352 686 $aSK 920$2rvk 700 $aAtkinson$b Kendall E.$054021 702 $aHan$b Weimin 702 $aStewart$b David$f1961- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910678196103321 996 $aNumerical solution of ordinary differential equations$91910730 997 $aUNINA