نتایج جستجو برای: Generalized Jacobi polynomials

تعداد نتایج: 208523  

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

Journal: :bulletin of the iranian mathematical society 0
m. behroozifar department of mathematics‎, ‎faculty of basic sciences‎, ‎babol noshirvani university of technology‎, ‎babol‎, ‎mazandaran‎, ‎iran. f. ahmadpour department of mathematics‎, ‎faculty of basic sciences‎, ‎babol noshirvani university of technology‎, ‎babol‎, ‎mazandaran‎, ‎iran.

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

Journal: :Bulletin of the American Mathematical Society 1936

Journal: :computational methods for differential equations 0
payam mokhtary department of mathematics, faculty of sciences, sahand university of technology, tabriz, iran. mahdiye gholipour department of mathematics, faculty of sciences, sahand university of technology, tabriz, iran.

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

Journal: :Computers & Mathematics with Applications 2003

Journal: :Transactions of the American Mathematical Society 1990

Journal: :J. Sci. Comput. 2006
Ben-yu Guo Jie Shen Li-Lian Wang

We extend the definition of the classical Jacobi polynomials withindexes α,β > −1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the...

2008
Ben-Yu Guo Jie Shen Li-Lian Wang

We introduce a family of generalized Jacobi polynomials/functions with indexes α,β ∈ R which are mutually orthogonal with respect to the corresponding Jacobi weights and which inherit selected important properties of the classical Jacobi polynomials. We establish their basic approximation properties in suitably weighted Sobolev spaces. As an example of their applications, we show that the gener...

Journal: :bulletin of the iranian mathematical society 2012
eid doha waleed mohammed abd-elhameed hany ahmed

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

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