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Boundary element methods in engineering and eciences / M. H. Aliabadi, P. Wen
Singapore : World Scientific, 2010
viii, 402 pages. ; 25 cm.
Ký hiệu phân loại (DDC): 620
The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique which has enjoyed increasing popularity over the past two decades. It is now an established alternative to traditional computational methods of engineering analysis. The main advantage of the BEM is its unique ability to provide a complete solution in terms of boundary values only, with substantial savings in modeling effort. This book is designed to provide readers with a comprehensive and up-to-date account of the method and its application to problems in engineering
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Lectures on the theory of group properties of differential equations / L. V. Ovsyannikov; N. Kh Ibragimov, E. D. Avdonina (editor)
Beijing : World Scientific, 2013
xi, 141 pages. ; 25 cm.
Ký hiệu phân loại (DDC): 515.3
These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models
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The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer
New Jersey : World Scientific, 2015
xv, 269 pages. : illustrations ; 25 cm.
Ký hiệu phân loại (DDC): 332.632
Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H. Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available. Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods
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