Numerical Methods for Engineers
Numerical Methods for Engineers
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DOI：
10.1201/9781420010244
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发表时间：
2006-06
期刊：
影响因子：
--
通讯作者：
D. V. Griffiths;I. Smith
中科院分区：
文献类型：
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作者：
D. V. Griffiths;I. Smith
介绍和编程序言介绍运行程序硬件外部Fortran子程序库一个简单的Fortran程序一些简单的Fortran结构内部函数用户-提供的函数和子程序误差和精度图形输出结论线性代数方程介绍高斯消元方程使用对称系数矩阵的因式分解方程求解带状方程可变带宽的紧凑存储旋转方程规定的解决方案迭代方法梯度方法非对称系统预处理比较直接和迭代方法练习非线性方程介绍迭代替换多根和其他困难插值方法外推法加速收敛系统的非线性方程练习本征值方程介绍向量迭代中间特征值通过收缩广义特征值问题[K] {x} =？[M]{x}变换方法特征多项式方法练习插值和曲线拟合介绍插值多项式插值使用三次样条函数数值微分曲线拟合练习数值积分介绍牛顿-科茨规则高斯-Legendre规则自适应积分规则特殊积分规则多重积分练习常微分方程的数值解介绍常微分方程初值问题的定义和类型边值问题练习介绍偏微分方程介绍偏微分方程的定义和类型一阶方程二阶方程有限差分法有限元法练习附录A：库子程序的描述附录B：Fortran 95库子程序列表附录C：参考文献和附加阅读
INTRODUCTION AND PROGRAMMING PRELIMINARIES Introduction Running Programs Hardware External Fortran Sub-Program Libraries A Simple Fortran Program Some Simple Fortran Constructs Intrinsic Functions User-Supplied Functions and Subroutines Errors and Accuracy Graphical Output Conclusions LINEAR ALGEBRAIC EQUATIONS Introduction Gaussian Elimination Equation Solution Using Factorization Equations with a Symmetrical Coefficient Matrix Banded Equations Compact Storage for Variable Bandwidths Pivoting Equations with Prescribed Solutions Iterative Methods Gradient Methods Unsymmetrical Systems Preconditioning Comparison of Direct and Iterative Methods Exercises NONLINEAR EQUATIONS Introduction Iterative Substitution Multiple Roots and Other Difficulties Interpolation Methods Extrapolation Methods Acceleration of Convergence Systems of Nonlinear Equations Exercises EIGENVALUE EQUATIONS Introduction Vector Iteration Intermediate Eigenvalues by Deflation The Generalized Eigenvalue Problem [K] {x} = ?[M] {x} Transformation Methods Characteristic Polynomial Methods Exercises INTERPOLATION AND CURVE FITTING Introduction Interpolating Polynomials Interpolation Using Cubic Spline Functions Numerical Differentiation Curve Fitting Exercises NUMERICAL INTEGRATION Introduction Newton-Cotes Rules Gauss-Legendre Rules Adaptive Integration Rules Special Integration Rules Multiple Integrals Exercises NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS Introduction Definitions and Types of ODE Initial Value Problems Boundary Value Problems Exercises INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS Introduction Definitions and Types of PDE First Order Equations Second Order Equations Finite Difference Method Finite Element Method Exercises APPENDIX A: Descriptions of Library Subprograms APPENDIX B: Fortran 95 Listings of Library Subprograms APPENDIX C: References and Additional Reading