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Intorduction
Numerical methods for complex systems
S. V. Gurevich
Intorduction
Definition, Notation and Classification
Linear Second-Order PDEs
Initial and Boundary-Value Problems
Finite difference method
The Taylor series method
Mixed derivatives
A nonequidistant mesh
Consistency, Convergence and Stability
Numerical Errors
Stability
von Neumann stability analysis
Hyperbolic PDE's
Wave equation
Wave equation in 1D
Solution of the initial value problem
A numerical scheme
An explicit method
Stability analysis
An implicit method
Examples
Example 1.
Example 2.
Example 3. Vibrating String
Wave Equation in 2D
Example 1.
Sine-Gordon equation
Numerical solution
A numerical scheme
Examples
About this document ...
Gurevich_Svetlana 2008-11-12
