LEADER 04901nam 2200613 450 001 9910464288703321 005 20200520144314.0 010 $a1-118-83890-4 010 $a1-118-83891-2 035 $a(CKB)3360000000479639 035 $a(EBL)1680800 035 $a(SSID)ssj0001289143 035 $a(PQKBManifestationID)11707754 035 $a(PQKBTitleCode)TC0001289143 035 $a(PQKBWorkID)11308468 035 $a(PQKB)11248372 035 $a(MiAaPQ)EBC1680800 035 $a(DLC) 2013045863 035 $a(Au-PeEL)EBL1680800 035 $a(CaPaEBR)ebr10913516 035 $a(CaONFJC)MIL769950 035 $a(OCoLC)863100793 035 $a(EXLCZ)993360000000479639 100 $a20140829h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to numerical methods for time dependent differential equations /$fHeinz-Otto Kreiss, Omar Eduardo Ortiz 210 1$aHoboken, New Jersey :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (314 p.) 300 $aDescription based upon print version of record. 311 $a1-118-83895-5 320 $aIncludes bibliographical references and index. 327 $aCover; Half Title page; Title page; Copyright page; Dedication; Preface; Acknowledgements; Part I: Ordinary Differential Equations and Their Approximations; Chapter 1: First-Order Scalar Equations; 1.1 Constant coefficient linear equations; 1.2 Variable coefficient linear equations; 1.3 Perturbations and the concept of stability; 1.4 Nonlinear equations: the possibility of blow-up; 1.5 Principle of linearization; Chapter 2: Method of Euler; 2.1 Explicit Euler method; 2.2 Stability of the explicit Euler method; 2.3 Accuracy and truncation error 327 $a2.4 Discrete Duhamel's principle and global error2.5 General one-step methods; 2.6 How to test the correctness of a program; 2.7 Extrapolation; Chapter 3: Higher-Order Methods; 3.1 Second-order Taylor method; 3.2 Improved Euler's method; 3.3 Accuracy of the solution computed; 3.4 Runge-Kutta methods; 3.5 Regions of stability; 3.6 Accuracy and truncation error; 3.7 Difference approximations for unstable problems; Chapter 4: Implicit Euler Method; 4.1 Stiff equations; 4.2 Implicit Euler method; 4.3 Simple variable-step-size strategy; Chapter 5: Two-Step and Multistep Methods 327 $a5.1 Multistep methods5.2 Leapfrog method; 5.3 Adams methods; 5.4 Stability of multistep methods; Chapter 6: Systems of Differential Equations; Part II: Partial Differential Equations and Their Approximations; Chapter 7: Fourier Series and Interpolation; 7.1 Fourier expansion; 7.2 L2-norm and scalar product; 7.3 Fourier interpolation; Chapter 8: 1-Periodic Solutions of time Dependent Partial Differential Equations with Constant Coefficients; 8.1 Examples of equations with simple wave solutions 327 $a8.2 Discussion of well posed problems for time dependent partial differential equations with constant coefficients and with 1-periodic boundary conditionsChapter 9: Approximations of 1-Periodic Solutions of Partial Differential Equations; 9.1 Approximations of space derivatives; 9.2 Differentiation of Periodic Functions; 9.3 Method of lines; 9.4 Time Discretizations and Stability Analysis; Chapter 10: Linear Initial Boundary Value Problems; 10.1 Well-Posed Initial Boundary Value Problems; 10.2 Method of lines; Chapter 11: Nonlinear Problems 327 $a11.1 Initial value problems for ordinary differential equations11.2 Existence theorems for nonlinear partial differential equations; 11.3 Nonlinear example: Burgers' equation; Appendix A: Auxiliary Material; A.1 Some useful Taylor series; A.2 "O" notation; A.3 Solution expansion; Appendix B: Solutions to Exercises; References; Index 330 $a Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamen 606 $aDifferential equations, Partial$xNumerical solutions 608 $aElectronic books. 615 0$aDifferential equations, Partial$xNumerical solutions. 676 $a515/.353 700 $aKreiss$b H$g(Heinz-Otto),$0898763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464288703321 996 $aIntroduction to numerical methods for time dependent differential equations$92007988 997 $aUNINA