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: A new algorithm is derived for the standard fixed-interval linear smoothing problem in which the signal is generated by a state model that allows the smoothed estimate to be easily updated in response to a change in the initial state covariance matrix.
Abstract: A new algorithm is derived for the standard fixed-interval linear smoothing problem in which the signal is generated by a state model. The structure of this new algorithm allows the smoothed estimate to be easily updated in response to a change in the initial state covariance matrix \Pi_{0} , since, unlike in existing algorifiuns, the relevant Riccati equation is entirely independent of \Pi_{0} . The derivation of the algorithm is based on properties of complementary models.
57 citations
TL;DR: In this paper, the generalized Schrodinger equation was solved numerically via the Crank-Nicholson scheme, and the stability and convergence of the space fractional variable-order Schroffinger equation were presented in detail.
Abstract: The space fractional Schrodinger equation was further extended to the concept of space fractional variable-order derivative. The generalized equation is very difficult to handle analytically. We solved the generalized equation numerically via the Crank-Nicholson scheme. The stability and the convergence of the space fractional variable-order Schrodinger equation were presented in detail.
57 citations
TL;DR: In this article, a definite theorem due to Lie which group theoretically characterizes those systems of ordinary differential equations which possess nonlinear superposition principles is employed along with an observation by Lie on the exponentiated form of a fibered Lie algebra to obtain an explicit expression for the Vessiot-Guldberg-Lie non linear superposition principle admitted by n-coupled Riccati equations of the projective type.
Abstract: A definite theorem due to Lie which group theoretically characterizes those systems of ordinary differential equations which possess nonlinear superposition principles is employed along with an observation by Lie on the exponentiated form of a fibered Lie algebra to obtain an explicit expression for the Vessiot-Guldberg-Lie nonlinear superposition principle admitted by n-coupled Riccati equations of the projective type. This also, immediately, yields an explicit expression for the generalized cross-ratio for the projective group in n-dimensions.
57 citations
TL;DR: In this paper, the authors proved global existence for the solution of a Riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations.
Abstract: Global existence is proved for the solution, of a Riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations.
57 citations
TL;DR: Two numerical techniques are presented for solving the solution of Riccati differential equation by expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions.
57 citations