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Differential equations and solution of linear systems
Numerical Algorithms, 2005Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution ...
Jacques Laminie +2 more
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1998
We denote ri x n matrices by uppercase italic letters, $$ A = \left( {\begin{array}{*{20}{c}} {{a_{11}} \ldots {a_{1n}}} \\ { \vdots \ddots \vdots } \\ {{a_{n1}} \cdots {a_{nn}}} \end{array}} \right) = ({a_{ij}}), $$ where aij E R or C. With the usual definitions of addition and scalar multiplication of matrices, $$ A + B = ({a_{ij}} + {b_ ...
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We denote ri x n matrices by uppercase italic letters, $$ A = \left( {\begin{array}{*{20}{c}} {{a_{11}} \ldots {a_{1n}}} \\ { \vdots \ddots \vdots } \\ {{a_{n1}} \cdots {a_{nn}}} \end{array}} \right) = ({a_{ij}}), $$ where aij E R or C. With the usual definitions of addition and scalar multiplication of matrices, $$ A + B = ({a_{ij}} + {b_ ...
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Second Order Linear Differential Equations
1975A second-order differential equation is an equation of the form $$\frac{{{d^2}y}}{{d{t^2}}} = f\left( {t,y,\frac{{dy}}{{dt}}} \right)$$ (1) .
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Linear Partial Differential Equations
1997Partial differential equations arise frequently in the formulation of fundamental laws of nature and in the mathematical analysis of a wide variety of problems in applied mathematics, mathematical physics, and engineering science. This subject plays a central role in modern mathematical sciences, especially in physics, geometry, and analysis.
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On linear differential-algebraic equations and linearizations
2005On the background of a careful analysis of linear DAEs, linearizations of nonlinear index-2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization ...
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Differential Privacy Techniques for Cyber Physical Systems: A Survey
IEEE Communications Surveys and Tutorials, 2020Jinjun Chen +2 more
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Hypercalcemia and cancer: Differential diagnosis and treatment
Ca-A Cancer Journal for Clinicians, 2018Sarah B Fisher, Nancy D Perrier
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