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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
Differential equations --- Equations différentielles --- Numerical solutions. --- Solutions numériques --- 519.6 --- 681.3*G17 --- Computational mathematics. Numerical analysis. Computer programming --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.91 Differential equations
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Imbedding is a powerful and versatile tool for problem solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.
Numerical solutions of differential equations --- Business & Economics --- Economic Theory --- 681.3*G17 --- 681.3*G19 --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Invariant imbedding --- Differential equations --- Integral equations --- Equations différentielles --- Equations intégrales --- Plongement invariant --- Équations aux dérivées partielles --- Programmation (mathématiques) --- Équations aux dérivées partielles --- Programmation (mathématiques) --- Equations differentielles
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517.97 --- 519.6 --- 681.3 *G18 --- 681.3*G17 --- Calculus of variations. Mathematical theory of control --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.97 Calculus of variations. Mathematical theory of control --- Physique mathématique --- Equations aux derivees partielles --- Methodes numeriques --- Methodes variationnelles
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Mathematics --- Differential equations --- Numerical integration --- Equations différentielles --- Data processing --- Informatique --- -Numerical integration --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.6 --- 681.3*G17 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- 517.91 Differential equations --- 517.91 --- Numerical solutions --- Data processing. --- Mathematics. --- Numerical solutions&delete& --- Differential equations - Data processing --- Numerical integration - Data processing --- Acqui 2006
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