Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: It is shown, via simple algebraic manipulations, that the key prediction equation used for GPC can be easily derived from the transfer function coefficients effectively replacing the Diophantine equation recursions by the inversion of a lower triangular matrix.
49 citations
TL;DR: In this paper, the Klein-Gordon equation is solved approximately for the Hulthen potential for any angular momentum quantum number l with the position-dependent mass, and the results in the case of constant mass are in good agreement with the ones obtained in the literature.
Abstract: The Klein-Gordon equation is solved approximately for the Hulthen potential for any angular momentum quantum number l with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a Schrodinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get an energy eigenvalue and and the wave functions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.
49 citations
TL;DR: In this paper, a modified tanh-coth method was used to solve the general Burgers-Fisher and the Kuramoto-Sivashinsky equations, taking full advantage of the Riccati equation that the tanh function satisfies.
49 citations
TL;DR: In this paper, for an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems.
Abstract: For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong onvergence of the approximating Riccati operators in case of a previously developed spline approximation scheme for delay systems is established. Finally, convergence of the transfer-functions of the approximating systems is investigated.
49 citations
TL;DR: Batchelder and Batchelder as discussed by the authors studied the irregular cases of the second-order equation of second order with coefficients linear in x, employing the Laplace transformation, and gave formal series solutions (divergent) and a theorem setting forth the existence of solutions with asymptotic forms for large real positive values of x.
Abstract: the assumption is commonly made that the roots of (3) are finite, distinct, and different from zero. This narrowly restrictive hypothesis characterizes what we call the regular case. But little attention has yet been devoted to the more general problem of the irregular cases, in which the roots fail to satisfy this hypothesis. Barnesf in 1905 studied most of the irregular cases of the equation of second order with coefficients linear in x, employing the Laplace transformation. In 1910 Horn| gave formal series solutions (divergent) and a theorem setting forth the existence of solutions whose asymptotic forms for large real positive values of x are given by the formal series, when the only departure from regularity is the vanishing of one root. In papers read (by title) before the Society in 1913 Batchelder§ found formal series solutions in all possible irregular cases for the equation of second
49 citations