Sixth-Order Adaptive Non-uniform Grids for Singularly Perturbed Boundary Value Problems

2019 ◽  
pp. 109-124
Author(s):  
Sehar Iqbal ◽  
Paul Andries Zegeling
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Sixth Order ◽  
Uniform Grids

scholarly journals New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
W. M. Abd-Elhameed
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
High Order ◽  
Sixth Order ◽  
Special Cases ◽  
Derivatives Of

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms.

Non-polynomial splines approach to the solution of sixth-order boundary-value problems

2008 ◽  
Vol 195 (1) ◽  
pp. 270-284 ◽  
Author(s):  
Siraj-ul-Islam ◽  
Ikram A. Tirmizi ◽  
Fazal-i-Haq ◽  
M. Azam Khan
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Polynomial Splines
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