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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.
a. Weak formulation with respect to time parameter.
b. Discretization with respect to time parameter.
c. Discretization for backward Kolmogorov equation.
d. Existence and uniqueness for time-discretized problem.
e. Convergence of discontinuous Galerkin technique. Adaptive time stepping.
C. Laplace quadrature.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Weak formulation with respect to time parameter.


n context of the condition ( Generic parabolic PDE setup ) we introduce the class MATH For any MATH , we apply the operation MATH to the equation ( Generic parabolic PDE problem ) and integrate over $\left[ 0,T\right] $ : MATH We integrate the first term by parts: MATH

Problem

(Weak formulation with respect to time parameter) In context of the condition ( Generic parabolic PDE setup ) we seek MATH such that

MATH (Time-weak problem)
for any MATH .





Notation. Index. Contents.


















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