Modelling Mathematical Methods and Scientific Computation
Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.
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analysis analytic solution applied approximation behavior bifurcation diagram boundary conditions Chapter Chebyshev classification coefficients collocation method compute Consider constant continuous defined DEFINITION derivative Dirichlet boundary conditions domain eigenvalues equilibrium configuration Euler method evolution equation Example fact finite difference first-order formulated fourth-order function given GOSUB GOTO heat equation Hopf bifurcation hyperbolic initial condition initial data initial-boundary-value problem initial-value problem instance integration interpolation interval inverse problems iprint limit cycle linear mathematical methods mathematical model mathematical problem matrix ndim ngraf nodes nonlinear norm obtained ordinary differential equations parabolic parameters partial differential equations physical system plot polynomial PRINT print-out probability density procedure prstop PSET pumax random variable reader real system refer REMARK Runge-Kutta method scheme second-order Section simulation solve spline stability region stable step stochastic subroutine suitable term tfin theorem tion u(ix ua(t Uin(x unstable values vector ymax ymin