Author | Evans, Gwynne A. author |
---|---|
Title | Numerical Methods for Partial Differential Equations [electronic resource] / by Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley |
Imprint | London : Springer London : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0377-6 |
Descript | XII, 290 p. online resource |
1. Background Mathematics -- 1.1 Introduction -- 1.2 Vector and Matrix Norms -- 1.3 Gerschgorinโs Theorems -- 1.4 Iterative Solution of Linear Algebraic Equations -- 1.5 Further Results on Eigenvalues and Eigenvectors -- 1.6 Classification of Second Order Partial Differential Equations -- 2. Finite Differences and Parabolic Equations -- 2.1 Finite Difference Approximations to Derivatives -- 2.2 Parabolic Equations -- 2.3 Local Truncation Error -- 2.4 Consistency -- 2.5 Convergence -- 2.6 Stability -- 2.7 The Crank-Nicolson Implicit Method -- 2.8 Parabolic Equations in Cylindrical and Spherical Polar Coordinates -- 3. Hyperbolic Equations and Characteristics -- 3.1 First Order Quasi-linear Equations -- 3.2 Lax-Wendroff and Wendroff Methods -- 3.3 Second Order Quasi-linear Hyperbolic Equations -- 3.4 Reetangular Nets and Finite Difference Methods for Second Order Hyperbolic Equations -- 4. Elliptic Equations -- 4.1 Laplaceโs Equation -- 4.2 Curved Boundaries -- 4.3 Solution of Sparse Systems of Linear Equations -- 5. Finite Element Method for Ordinary Differential Equations -- 5.1 Introduction -- 5.2 The Collocation Method -- 5.3 The Least Squares Method -- 5.4 The Galerkin Method -- 5.5 Symmetrie Variational Forrnulation -- 5.6 Finite Element Method -- 5.7 Some Worked Examples -- 6. Finite Elements for Partial Differential Equations -- 6.1 Introduction -- 6.2 Variational Methods -- 6.3 Some Specific Elements -- 6.4 Assembly of the Elements -- 6.5 Worked Example -- 6.6 A General Variational Principle -- 6.7 Assembly and Solution -- 6.8 Solution of the Worked Example -- 6.9 Further Interpolation Functions -- 6.10 Quadrature Methods and Storage Considerations -- 6.11 Boundary Element Method -- A. Solutions to Exercises -- References and Further Reading