Comparing the Performance of Four Sinc Methods for Numerical Indefinite Integration

Aims/ Objectives: To compare the performance of four Sinc methods for the numerical approximation of indefinite integrals with algebraic or logarithmic end-point singularities. Methodology: The first two quadrature formulas were proposed by Haber based on the sinc method, the third is Stengers Single Exponential (SE) formula and Tanaka et al.s Double Exponential (DE) sinc method completes the number. Furthermore, an application of the four quadrature formulas on numerical examples, reveals convergence to the exact solution by Tanaka et al.s DE sinc method than by the other three formulae. In addition, we compared the CPU time of the four quadrature methods which was not done in an earlier work by the same author. Conclusion: Haber formula A is the fastest as revealed by the CPU time.

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

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

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

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.

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, 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.