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偏微分方程地构建科学、工程学和其他领域的数学模型的主要手段。一般情况下，这些模型都需要用数值方法去求解。本书提供了标准数值技术的简明介绍。借助抛物线型、双曲线型和椭圆型方程的一些简单例子介绍了常用的有限差分方法、有限元方法、有限体方法、修正方程分析、辛积分格式、对流扩散问题、多重网络、共轭梯度法。利用极大值原理、能量法和离散傅里叶分析清晰严格地处理了稳定性问题。本书全面讨论了这些方法的性质，并附有典型的图像结果，提供了不同难度的例子和练习。

本书可作为数学、工程学及计算机科学专业本科教材，也可供工程技术人员和应用工作者参考。

K.W.Morton，牛津大学退休教授，曾任教于数值分析学术重镇牛津大学计算实验室。现为巴斯大学兼职教授。主要研究领域为有限差分、有限元和有限体方法。Morton有着丰富的教学经验，他存数值分析领域的理论研究和实际应用方面的成就也广为人知。他曾担任数值分析界最高荣誉Leslie Fox奖评委会主席。

D.F.Mayers，曾任职于牛津大学计算实验室，是已故数值分析先驱Leslie Fox的长期合作者。除本书之外，他还著有广泛采用的教材An Introduetio to Numerical Analysis。

1 Introduction2 Parabolic equations in one space variable 2.1 Introduction 2.2 A model problem 2.3 Series approximation 2.4 An explicit scheme for the model problem 2.5 Difference notation and truncation error 2.6 Convergence of the explicit scheme 2.7 Fourier analysis of the error 2.8 An implicit method 2.9 The Thomas algorithm 2.10 The weighted average or 0.method 2.11 A maximum principle and convergence 2.12 A three.time.level scheme 2.13 More general boundary conditions 2.14 Heat conservation properties 2.15 More general linear problems 2.16 Polar co.ordinates 2.17 Nonlinear problems Bibliographic notes Exercises3 2.D and 3.D parabolic equations 3.1 The explicit method in a rectilinear box 3.2 An ADI method in two dimensions 3.3 ADI and LOD methods in three dimensions 3.4 Curved boundaries 3.5 Application to general parabolic problems Bibliographic notes Exercises4 Hyperbolic equations in one space dimension 4.1 Characteristics 4.2 The CFL condition 4.3 Error analysis of the upwind scheme 4.4 Fourier analysis of the upwind scheme 4.5 The Lax.Wendroff scheme 4.6 The Lax.Wendroff method for conservation laws 4.7 Finite volume schemes 4.8 The box scheme 4.9 The leap.frog scheme 4.10 Hamiltonian systems and symplectic integration schemes 4.11 Comparison of phase and amplitude errors 4.12 Boundary conditions and conservation properties 4.13 Extensions to more space dimensions Bibliographic notes Exercises5 Consistency, convergence and stability 5.1 Definition of the problems considered 5.2 The finite difference mesh and norms 5.3 Finite difference approximations 5.4 Consistency, order of accuracy and convergence 5.5 Stability and the Lax Equivalence Theorem 5.6 Calculating stability conditions 5.7 Practical (strict or strong) stability 5.8 Modified equation analysis 5.9 Conservation laws and the energy method of analysis 5.10 Summary of the theory Bibliographic notes Exercises 6 Linear second order elliptic equations in two dimensions 6.1 A model problem 6.2 Error analysis of the model problem 6.3 The general diffusion equation 6.4 Boundary conditions on a curved boundary 6.5 Error analysis using a maximum principle 6.6 Asymptotic error estimates 6.7 Variational formulation and the finite element method 6.8 Convection.diffusion problems 6.9 An example Bibliographic notes Exercises7 Iterative solution of linear algebraic equations 7.1 Basic iterative schemes in explicit form 7.2 Matrix form of iteration methods and their convergence 7.3 Fourier analysis of convergence 7.4 Application to an example 7.5 Extensions and related iterative methods 7.6 The multigrid method 7.7 The conjugate gradient method 7.8 A numerical example: comparisons Bibliographic notes ExercisesReferencesIndex
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