Complex contour integral representations of cardinal spline functions

1982 ◽  
Author(s):  
Walter Schempp
Keyword(s):  
Integral Representations ◽  
Contour Integral ◽  
Spline Functions ◽  
Complex Contour ◽  
Cardinal Spline

scholarly journals On A Logarithmic Mittag-Leffler Function, its Properties and Applications

2021 ◽  
Author(s):  
M.A. Pathan ◽  
Hemant Kumar
Keyword(s):  
Infectious Diseases ◽  
Hypergeometric Functions ◽  
Point Of View ◽  
Integral Representations ◽  
Contour Integral ◽  
Application Point

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions. 

scholarly journals The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaoyan Liu ◽  
Jin Xie ◽  
Zhi Liu ◽  
Jiahuan Huang
Keyword(s):  
Integral Equations ◽  
High Accuracy ◽  
Spline Functions ◽  
Sufficient Condition ◽  
Nonlinear Integral Equations ◽  
Effective Technique ◽  
Original Solution ◽  
Cardinal Spline ◽  
The Matrix ◽  
Cardinal Splines

In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. Several cardinal splines are employed in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined, and the convergence rate is analyzed. We compare our method with other methods proposed in recent papers and demonstrated the advantage of our method with several examples.

Identification of MIMO Hammerstein systems using cardinal spline functions

2006 ◽  
Vol 16 (7) ◽  
pp. 659-670 ◽  
Author(s):  
Kwong Ho Chan ◽  
Jie Bao ◽  
William J. Whiten
Keyword(s):  
Spline Functions ◽  
Hammerstein Systems ◽  
Cardinal Spline
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