G. Evans, J. Blackledge and P. Yardley
Numerical Methods
for Partial Differential
Equations
With 55 Figures
Springer

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*Sign up*Contents
1. Background Mathematics
1
1.1 Introduction
1
1.2 Vector and Matrix Norms
3
1.3 Gerschgorin's Theorems
7
1.4 Iterative Solution of Linear Algebraic Equations
10
1.5 Further Results on Eigenvalues and Eigenvectors
18
1.6 Classification of Second Order Partial Differential Equations .
.. 23
2. Finite Differences and Parabolic Equations
29
2.1 Finite Difference Approximations to Derivatives
29
2.2 Parabolic Equations
34
2.3 Local Truncation Error
41
2.4 Consistency
43
2.5 Convergence
46
2.6 Stability
48
2.7 The Crank-Nicolson Implicit Method
54
2.8 Parabolic Equations in Cylindrical and Spherical Polar Coor-
dinates
59
3. Hyperbolic Equations and Characteristics
67
3.1 First Order Quasi-linear Equations
67
3.2 Lax-Wendroff and Wendroff Methods
72
3.3 Second Order Quasi-linear Hyperbolic Equations
80
3.4 Rectangular Nets and Finite Difference Methods for Second
Order Hyperbolic Equations

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