微分方程数值方法引论作 者: (美)霍姆斯 编著出版时间:2011内容简介 《微分方程数值方法引论》内容包括:初值问题、两点边界值问题、扩散问题、平流方程、椭圆型问题等。目录Preface1 Initial Value Problems 1.1 Introduction 1.1.1 Examples of IVPs 1.2 Methods Obtained from Numerical Differentiation . 1.2.1 The Five Steps 1.2.2 Additional Difference Methods 1.3 Methods Obtained from Numerical Quadrature 1.4 Runge--Kutta Methods 1.5 Extensions and Ghost Points 1.6 Conservative Methods 1.6.1 Velocity Verlet 1.6.2 Symplectic Methods 1.7 Next Steps Exercises2 Two-Point Boundary Value Problems 2.1 Introduction 2.1.1 Birds on a Wire 2.1.2 Chemical Kinetics 2.2 Derivative Approximation Methods 2.2.1 Matrix Problem 2.2.2 Tridiagonal Matrices 2.2.3 Matrix Problem Revisited 2.2.4 Error Analysis 2.2.5 Extensions 2.3 Residual Methods 2.3.1 Basis Functions 2.3.2 Residual 2.4 Shooting Methods 2.5 Next Steps Exercises3 Diffusion Problems 3.1 Introduction 3.1.1 Heat Equation 3.2 Derivative Approximation Methods 3.2.1 Implicit Method 3.2.2 Theta Method 3.3 Methods Obtained from Numerical Quadrature 3.3.1 Crank-Nicolson Method 3.3.2 L-Stability 3.4 Methods of Lines 3.5 Collocation 3.6 Next Steps Exercises4 Advection Equation 4.1 Introduction 4.1.1 Method of Characteristics 4.1.2 Solution Properties 4.1.3 Boundary Conditions 4.2 First-Order Methods 4.2.1 Upwind Scheme 4.2.2 Downwind Scheme 4.2.3 blumericul Domu'm of Dependence 4.2.4 Stability 4.3 Improvements 4.3.1 Lax-Wendroff Method 4.3.2 Monotone Methods 4.3.3 Upwind Revisited 4.4 Implicit Methods Exercises5 Numerical Wave Propagation 5.1 Introduction 5.1.1 Solution Methods 5.1.2 Plane Wave Solutions 5.2 Explicit Method 5.2.1 Diagnostics 5.2.2 Numerical Experiments 5.3 Numerical Plane Waves 5.3.1 Numerical Group Velocity 5.4 Next Steps Exercises6 Elliptic Problems 6.1 Introduction 6.1.1 Solutions 6.1.2 Properties of the Solution 6.2 Finite Difference Approximation 6.2.1 Building the Matrix 6.2.2 Positive Definite Matrices 6.3 Descent Methods 6.3.1 Steepest Descent Method 6.3.2 Conjugate Gradient Method 6.4 Numerical Solution of Laplace's Equation 6.5 Preconditioned Conjugate Gradient Method 6.6 Next Steps ExercisesA Appendix A.1 Order Symbols A.2 Taylor's Theorem A.3 Round-Off Error A.3.1 Fhnction Evaluation A.3.2 Numerical Differentiation A.4 Floating-Point NumbersReferencesIndex 上一篇: 数学建模方法与数学实验 下一篇: 2015考研专家指导丛书:考研数学最后冲刺超越135分(数学二)