3 edition of Legendre-Tau approximation for functional differential equations. found in the catalog.
Legendre-Tau approximation for functional differential equations.
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
Written in English
|Statement||Kazufumi Ito, Russell Teglas.|
|Series||ICASE report -- no. 84-31., NASA contractor report -- NASA CR-172397.|
|Contributions||Teglas, Russell., Langley Research Center., Institute for Computer Applications in Science and Engineering.|
|The Physical Object|
Deriving the Regression Equation without Using Calculus. ERIC Educational Resources Information Center. Gordon, Sheldon P.; Gordon, Florence S. Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data . The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation.
is solved by tau approximation using Legendre polynomials. The Mh degree Legendre-tau approximation UN satisfies which proves stability, (ii) Suppose that is solved by the tau method using Chebyshev polynomials. Since L =82/Bx2 is degree reducing and L +L*^0 [see Example (v)), the method is stable, (iii) The solution of. Classification of functional differential equations Assume that max = const [0,), and let x(t) be an n-dimensional variable describing the behaviour of a process in the time interval t [t0 max, t1].
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In this paper we consider the numerical approximation of solutions to linear retarded functional differential equations using the so-called Legendre–tau method.
The Cited by: Ito K. () Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability. In: Kappel F., Kunisch K., Schappacher W.
(eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol Springer, Berlin, Heidelberg. First Online 29 September Cited by: 5.
Get this from a library. Legendre-Tau approximation for functional differential equations Part III, Eigenvalue approximations and uniform stability. [Kazufumi Ito; Langley Research Center.].
Get this from a library. Legendre-Tau approximation for functional differential equations. Part II, The linear quadratic optimal control problem. [Kazufumi Ito; Russell Teglas; Langley Research Center.; Institute for Computer Applications in Science and Engineering.]. Legendre-Tau Approximation for Functional Differential Equations Part II: The Linear Quadratic Optimal Control Problem Article (PDF Available) in SIAM Journal on.
The main result obtained in this study is the following operational Tau method based on Müntz-Legendre polynomials.
This method provides a computational technique for. A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations A free fractional viscous oscillator as a forced standard damped vibration On a Legendre Tau method for fractional boundary value problems with a Caputo derivativeCited by: 3.
Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability. Distributed Parameter Systems, Asymptotically perfect reconstruction in hybrid filter by: Distributed Parameter Systems Proceedings of the 2nd International Conference Vorau, Austria Editors; Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability.
Differential stability of control constrained optimal control problems for distributed parameter systems. Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability Differential stability of control constrained optimal control problems for distributed parameter systems.
Distributed Parameter Systems Book Subtitle Proceedings of the 2nd International Conference Vorau, Austria The essential target of this paper is to recommend a suitable way to approximate FFDEs using a shifted Legendre tau approach. This strategy demands a formula for fuzzy fractional-order Caputo derivatives of shifted Legendre polynomials of any degree which is provided and applied together with the tau method for solving FFDEs with initial Cited by: This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs).
We work in Hilbert spaces endowed with a natural inner product including a point mass, and introduce polynomials orthogonal with respect to such an inner product that live in the domain of the linear operator associated with Cited by: A truncated Legendre series together with generalized Legendre operational matrix is used to solve fractional differential equations by Saadatmandi and Dehgan in and they also have presented shifted Legendre-tau method for finding the solution of fractional diffusion equations with variable coefficients in.
In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing the fractional Taylor operational matrix of fractional integration.
This system of equations can be solved efficiently. A new operational matrix for solving fractional-order differential equations. Author links open overlay panel Abbas calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations.
For that reason we need a reliable and efficient technique for the solution of Cited by: Luis F. Cordero and René Escalante, Segmented Tau approximation for test neutral functional differential equations, Applied Mathematics and Computation,2, (), ().
Crossref R. Grundy, Hermite interpolation visits ordinary two-point boundary value problems, The ANZIAM Journal, /S, 48, 4, ( Cited by: The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions.
A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey. This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory.
The computational side vigorously since the early s, especially in computationally intensive of the more spectacular applications are. A survey on fuzzy fractional differential and optimal control nonlocal evolution equations Author links open overlay panel Ravi P. Agarwal a Dumitru Baleanu b c Juan J.
Nieto d Delfim F.M. Torres e Yong Zhou f gCited by: The Müntz-Legendre Tau method for fractional differential equations P. Mokhtary, F. Ghoreishi, and H.M. Srivastava Applied Mathematical Modelling, Cited by:.
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We achieve this by working closely with our society partners, authors, and subscribers in order to provide them with publishing services that support their research needs.H. M. Srivastava, I. Kucukoǧlu, and Y. Simsek, Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials, J.
Number Theory (), J. Andrzej Domaradzki and Steven A. Orszag Numerical solutions of the direct interaction approximation equations for solution of steady-state and transient nonlinear partial differential equations C.
Trayner and M. H Journal of Scientific Computing.