271269243 - G Evans J Blackledge and P Yardley Numerical...

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G. Evans, J. Blackledge and P. Yardley Numerical Methods for Partial Differential Equations With 55 Figures Springer
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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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271269243 - G Evans J Blackledge and P Yardley Numerical...

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