Partial Differential Equations with Numerical MethodsSpringer Science & Business Media, 5 dec. 2008 - 262 sidor The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. |
Innehåll
Introduction | 1 |
A TwoPoint Boundary Value Problem | 11 |
1 | 18 |
1 | 25 |
5 | 31 |
Problems | 73 |
The Elliptic Eigenvalue Problem | 77 |
InitialValue Problems for ODEs | 95 |
The Finite Element Method for a Parabolic Problem | 149 |
Hyperbolic Equations 163 | 162 |
Finite Difference Methods for Hyperbolic Equations | 185 |
The Finite Element Method for Hyperbolic Equations | 200 |
Some Other Classes of Numerical Methods | 217 |
A Some Tools from Mathematical Analysis | 225 |
B Orientation on Numerical Linear Algebra | 245 |
252 | |
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