An Overview of the Computation of the Eigenvalues Using Sinc-Methods

2020 ◽  
pp. 255-298
Author(s):  
M. H. Annaby ◽  
R. M. Asharabi ◽  
M. M. Tharwat
Keyword(s):  
Sinc Methods

Troesch’s problem solved by Sinc methods

2019 ◽  
Vol 162 ◽  
pp. 31-44
Author(s):  
Maha Youssef ◽  
Gerd Baumann
Keyword(s):  
Sinc Methods ◽  
Troesch’S Problem

Multigrid-sinc methods

1986 ◽  
Vol 19 (1-4) ◽  
pp. 311-319 ◽  
Author(s):  
Steve Schaffer ◽  
Frank Stenger
Keyword(s):  
Sinc Methods

scholarly journals Sinc-Self-consistent method to solve a class of nonlinear eigenvalue differential equation

2021 ◽  
Author(s):  
Seyed Mohammad Ali Aleomraninejad ◽  
Mehdi Solaimani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Subsequent Development ◽  
The Self ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Smallest Eigenvalue ◽  
Sinc Methods ◽  
Self Consistent ◽  
Consistent Method

In this paper, we combine the sinc and self-consistent methods to solve a class of non-linear eigenvalue differential equations. Some properties of the self-consistent and sinc methods required for our subsequent development are given and employed. Numerical examples are included to demonstrate the validity and applicability of the introduced technique and a comparison is made with the existing results. The method is easy to implement and yields accurate results. We show that the sinc-self-consistent method can solve the equations on an infinite domain and produces the smallest eigenvalue with the most accuracy

Fractional calculus and Sinc methods

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Gerd Baumann ◽  
Frank Stenger
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Integral Equations ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Fractional Integrals ◽  
Sinc Methods ◽  
Weakly Singular Integral Equations ◽  
Fractional Differential

AbstractFractional integrals, fractional derivatives, fractional integral equations, and fractional differential equations are numerically solved by Sinc methods. Sinc methods are able to deal with singularities of the weakly singular integral equations of Riemann-Liouville and Caputo type. The convergence of the numerical method is numerically examined and shows exponential behavior. Different examples are used to demonstrate the effective derivation of numerical solutions for different types of fractional differential and integral equations, linear and non-linear ones. Equations of mixed ordinary and fractional derivatives, integro-differential equations are solved using Sinc methods. We demonstrate that the numerical calculation needed in fractional calculus can be gained with high accuracy using Sinc methods.

Advection-diffusion equations: Temporal sinc methods

1995 ◽  
Vol 11 (4) ◽  
pp. 399-422 ◽  
Author(s):  
Kenneth L. Bowers ◽  
Timothy S. Carlson ◽  
John Lund
Keyword(s):  
Diffusion Equations ◽  
Sinc Methods ◽  
Advection Diffusion

scholarly journals Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

2021 ◽  
Vol 5 (2) ◽  
pp. 43
Author(s):  
Gerd Baumann
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Numerical Approximation ◽  
Laplace Transforms ◽  
Inverse Laplace Transform ◽  
Exact Methods ◽  
Sinc Methods ◽  
Fractional Differential

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

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