微分方程数值方法引论_PDF下载[141MB-百度云]--

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This book shows how to derive，test and analyze numerical methods for solving differential equations，including both ordinary and partial differential equations.The objective is that students learto solve differential equations numerically and understand the mathematical and computational issues that arise whethis is done. Includes aextensive collectioof exercises，which develop both the analytical and computational aspects of the material. Iadditioto more tha100 illustrations，the book includes a large collectioof supplemental material： exercise sets，MATLAB computer codes for both student and instructor，lecture slides and movies.

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Preface1 Initial Value Problems1．1 Introduction1．1．1 Examples of IVPs1．2 Methods Obtained from Numerical Differentiation．1．2．1 The Five Steps1．2．2 Additional Difference Methods1．3 Methods Obtained from Numerical Quadrature1．4 Runge——Kutta Methods1．5 Extensions and Ghost Points1．6 Conservative Methods1．6．1 Velocity Verlet1．6．2 Symplectic Methods1．7 Next StepsExercises2 Two-Point Boundary Value Problems2．1 Introduction2．1．1 Birds oa Wire2．1．2 Chemical Kinetics2．2 Derivative ApproximatioMethods2．2．1 Matrix Problem2．2．2 Tridiagonal Matrices2．2．3 Matrix Problem Revisited2．2．4 Error Analysis2．2．5 Extensions2．3 Residual Methods2．3．1 Basis Functions2．3．2 Residual2．4 Shooting Methods2．5 Next StepsExercises3 DiffusioProblems3．1 Introduction3．1．1 Heat Equation3．2 Derivative ApproximatioMethods3．2．1 Implicit Method3．2．2 Theta Method3．3 Methods Obtained from Numerical Quadrature3．3．1 Crank-NicolsoMethod3．3．2 L-Stability3．4 Methods of Lines3．5 Collocation3．6 Next StepsExercises4 AdvectioEquation4．1 Introduction4．1．1 Method of Characteristics4．1．2 SolutioProperties4．1．3 Boundary Conditions4．2 First-Order Methods4．2．1 Upwind Scheme4．2．2 Downwind Scheme4．2．3 blumericul Domu’m of Dependence4．2．4 Stability4．3 Improvements4．3．1 Lax-Wendroff Method4．3．2 Monotone Methods4．3．3 Upwind Revisited4．4 Implicit MethodsExercises5 Numerical Wave Propagation5．1 Introduction5．1．1 SolutioMethods5．1．2 Plane Wave Solutions5．2 Explicit Method5．2．1 Diagnostics5．2．2 Numerical Experiments5．3 Numerical Plane Waves5．3．1 Numerical Group Velocity5．4 Next StepsExercises6 Elliptic Problems6．1 Introduction6．1．1 Solutions6．1．2 Properties of the Solution6．2 Finite Difference Approximation6．2．1 Building the Matrix6．2．2 Positive Definite Matrices6．3 Descent Methods6．3．1 Steepest Descent Method6．3．2 Conjugate Gradient Method6．4 Numerical Solutioof Laplace’s Equation6．5 Preconditioned Conjugate Gradient Method6．6 Next StepsExercisesA AppendixA．1 Order SymbolsA．2 Taylor’s TheoremA．3 Round-Off ErrorA．3．1 FhnctioEvaluationA．3．2 Numerical DifferentiationA．4 Floating-Point NumbersReferencesIndex