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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Boundary value problems --- Initial value problems --- Invariant imbedding. --- Problèmes aux limites --- Plongement invariant --- Numerical solutions. --- Solutions numériques --- Invariant imbedding --- Numerical solutions --- 517.95 --- -Initial value problems --- -Invariant imbedding --- Functional equations --- Invariants --- Mathematical physics --- Radiation --- Problems, Initial value --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Partial differential equations --- 517.95 Partial differential equations --- Numerical analysis --- Boundary value problems - Numerical solutions --- Initial value problems - Numerical solutions --- Equations differentielles ordinaires --- Equations differentielles --- Problemes aux limites
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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank.
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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.
Derivative securities --- Options (Finance) --- Bonds --- Discrete-time systems. --- Differential equations, Partial. --- Mathematical models.
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