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 approximation behavior bifurcation diagram boundary conditions Chapter Chebyshev classification coefficients collocation collocation method compute Consider defined DEFINITION derivative Dirichlet boundary conditions discrete domain dynamic Eacample eigenvalues equilibrium configuration example extrema fact finite difference flag fourth-order function given GOSUB GOTO heat equation Hopf bifurcation hyperbolic initial condition initial data initial-boundary-value problem initial-value problem instance integration interval inverse problems iprint ı ı ı kgraf2 limit cycle linear mathematical methods mathematical model mathematical problem ngraf nodes nonlinear norm obtained ordinary differential equations parabolic parameters partial differential equations phase3 physical system plot polynomial PRINT print-out prstop PSET pumax pumin random variable reader refer REM REM REM REMARK Runge–Kutta Runge–Kutta method scheme Section solved space spline stable step stochastic subroutine T0 ndim T0 nx term theorem tion tſin u(ix unstable usug values vector ymax ymin
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