Stochastic differential equations have many applications in the
natural sciences. Besides, the employment of probabilistic
representations together with the Monte Carlo technique allows us
to reduce solution of multi-dimensional problems for partial
differential equations to integration of stochastic equations. This
approach leads to powerful computational mathematics that is
presented in the treatise. The authors propose many new special
schemes, some published here for the first time. In the second part
of the book they construct numerical methods for solving
complicated problems for partial differential equations occurring
in practical applications, both linear and nonlinear. All the
methods are presented with proofs and hence founded on rigorous
reasoning, thus giving the book textbook potential. An overwhelming
majority of the methods are accompanied by the corresponding
numerical algorithms which are ready for implementation in
practice. The book addresses researchers and graduate students in
numerical analysis, physics, chemistry, and engineering as well as
mathematical biology and financial mathematics.
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