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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
A. Change of variables for parabolic equation.
B. Discontinuous Galerkin technique.
C. Laplace quadrature.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Time discretization.


he section ( Finite element ) covers transforming parabolic PDE into a multidimensional ODE. In this section we treat time discretization. There are two different situations. If the spacial operator is not dependent on time then there is a technique that resolves the problem in few steps that may be executed in parallel. If the spacial operator does depend on time then there is a time-stepping procedure that is significantly less efficient than the time-independent technique. For this reason we first remark on possibility to remove time dependency from the spacial operator.




A. Change of variables for parabolic equation.
B. Discontinuous Galerkin technique.
C. Laplace quadrature.

Notation. Index. Contents.


















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