LEADER 04872nam 2200673 450 001 9910460739403321 005 20200520144314.0 010 $a1-119-01846-3 010 $a1-119-01845-5 035 $a(CKB)3710000000498431 035 $a(EBL)4040556 035 $a(SSID)ssj0001569186 035 $a(PQKBManifestationID)16221874 035 $a(PQKBTitleCode)TC0001569186 035 $a(PQKBWorkID)14835913 035 $a(PQKB)10719814 035 $a(PQKBManifestationID)16232292 035 $a(PQKB)21246189 035 $a(MiAaPQ)EBC4040556 035 $a(DLC) 2015019447 035 $a(Au-PeEL)EBL4040556 035 $a(CaPaEBR)ebr11113716 035 $a(CaONFJC)MIL902559 035 $a(OCoLC)929527905 035 $a(EXLCZ)993710000000498431 100 $a20151113h20162016 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to computation and modeling for differential equations /$fLennart Edsberg 205 $aSecond edition. 210 1$aHoboken, New Jersey :$cWiley,$d2016. 210 4$dİ2016 215 $a1 online resource (328 p.) 300 $aDescription based upon print version of record. 311 $a1-119-01844-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a""Title Page""; ""Copyright""; ""Table of Contents""; ""Preface""; ""Chapter 1: Introduction""; ""1.1 What is a Differential Equation?""; ""1.2 Examples of an ordinary and a partial differential equation""; ""1.3 Numerical analysis, a necessity for scientific computing""; ""1.4 Outline of the contents of this book""; ""Bibliography""; ""Chapter 2: Ordinary Differential Equations""; ""2.1 Problem Classification""; ""2.2 Linear Systems of Odes With Constant Coefficients""; ""2.3 Some Stability Concepts For Ode""; ""2.4 Some ode models in science and engineering"" 327 $a""2.5 Some Examples From Applications""""Bibliography""; ""Chapter 3: Numerical Methods For Initial Value Problems""; ""3.1 Graphical Representation Of Solutions""; ""3.2 Basic Principles Of Numerical Approximation Of ODE""; ""3.3 Numerical Solution Of IVP with euler' method""; ""3.4 Higher order methods for the IVP""; ""3.5 Special Methods For Special Problems""; ""3.6 The Variational Equation And Parameter Fitting In IVP""; ""Bibliography""; ""Chapter 4: Numerical methods for boundary value problems""; ""4.1 Applications""; ""4.2 Difference methods for BVP""; ""4.3 Ansatz methods for BVP"" 327 $a""Bibliography""""Chapter 5: Partial differential equations""; ""5.1 Classical PDE problems""; ""5.2 Differential operators used for PDEs""; ""5.3 Some PDE in science and engineering""; ""5.4 Initial and boundary conditions for PDE""; ""5.5 Numerical solution of PDEs, some general comments""; ""Bibliography""; ""Chapter 6: Numerical Methods for Parabolic Partial Differential Equations""; ""6.1 Applications""; ""6.2 An introductory example of discretization""; ""6.3 THE METHOD OF LINES FOR PARABOLIC PDEs""; ""6.4 Generalizations of the heat equation"" 327 $a""6.5 Ansatz methods for the model equation""""Bibliography""; ""Chapter 7: Numerical methods for elliptic partial differential equations""; ""7.1 Applications""; ""7.2 The finite difference method""; ""7.3 Discretization of a problem with different BCs""; ""7.4 ANSATZ Methods For Elliptic PDE""; ""Bibliography""; ""Chapter 8: Numerical methods for hyperbolic PDE""; ""8.1 Applications""; ""8.2 Numerical solution of hyperbolic PDE""; ""8.3 The Finite Volume Method""; ""8.4 Some examples of stability analysis for hyperbolic PDE""; ""Bibliography"" 327 $a""Chapter 9: Mathematical Modeling with Differential Equations""""9.1 NATURE LAWS""; ""9.2 CONSTITUTIVE EQUATIONS""; ""9.3 CONSERVATIVE EQUATIONS""; ""9.4 SCALING OF DIFFERENTIAL EQUATIONS TO DIMENSIONLESS FORM""; ""Chapter 10: Applied Projects On Differential Equations""; ""Appendix A: Some Numerical and Mathematical Tools""; ""A.1 Newton's Method for Systems of Nonlinear Algebraic Equations""; ""A.2 Some Facts about Linear Difference Equations""; ""A.3 Derivation of Difference Approximations""; ""Bibliography""; ""A.4 THE INTERPRETATIONS OF GRAD, DIV, AND CURL"" 327 $a""A.5 NUMERICAL SOLUTION OF ALGEBRAIC SYSTEMS OF EQUATIONS"" 606 $aDifferential equations$xData processing 606 $aMathematical models 608 $aElectronic books. 615 0$aDifferential equations$xData processing. 615 0$aMathematical models. 676 $a515/.350285 700 $aEdsberg$b Lennart$f1946-$0917290 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910460739403321 996 $aIntroduction to computation and modeling for differential equations$92056467 997 $aUNINA