Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

In this paper, it is presented that an approximate solution of a class of non-linear differential equations with conformable derivative under boundary conditions by using sinc-Galerkin method that is not used to approximately solve the class of the considered equation in the literature. In the method, the solution function is expressed as a finite series in terms of composite translated sinc functions and the unknown coefficients. The problem is reduced into a non-linear matrix-vector system via sinc grid points, and when this system is solved by using Newton?s method, the unknown coefficients of the solution function are easily obtained. Also, error analysis and some test problems are presented to illustrate the applicability and accuracy of the proposed method.

Robust Deep Speaker Recognition: Learning Latent Representation with Joint Angular Margin Loss

Speaker identification is gaining popularity, with notable applications in security, automation, and authentication. For speaker identification, deep-convolutional-network-based approaches, such as SincNet, are used as an alternative to i-vectors. Convolution performed by parameterized sinc functions in SincNet demonstrated superior results in this area. This system optimizes softmax loss, which is integrated in the classification layer that is responsible for making predictions. Since the nature of this loss is only to increase interclass distance, it is not always an optimal design choice for biometric-authentication tasks such as face and speaker recognition. To overcome the aforementioned issues, this study proposes a family of models that improve upon the state-of-the-art SincNet model. Proposed models AF-SincNet, Ensemble-SincNet, and ALL-SincNet serve as a potential successor to the successful SincNet model. The proposed models are compared on a number of speaker-recognition datasets, such as TIMIT and LibriSpeech, with their own unique challenges. Performance improvements are demonstrated compared to competitive baselines. In interdataset evaluation, the best reported model not only consistently outperformed the baselines and current prior models, but also generalized well on unseen and diverse tasks such as Bengali speaker recognition.

Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations

In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.

DOUBLE EXPONENTIAL EULER–SINC COLLOCATION METHOD FOR A TIME–FRACTIONAL CONVECTION–DIFFUSION EQUATION

In this research, a new version of Sinc-collocation method incorporated with a Double Exponential (DE) transformation is implemented for a class of convectiondiffusion equations that involve time fractional derivative in the Caputo sense. Our approach uses the DE Sinc functions in space and the Euler polynomials in time, respectively. The problem is reduced to the solution of a system of linear algebraic equations. A comparison between the proposed approximated solution and numerical/exact/available solution reveals the reliability and significant advantages of our newly proposed method.

Numerical Wave Solutions for Nonlinear Coupled Equations using Sinc-Collocation Method

In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to discretize time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Solving nonlinear boundary value problems by the Galerkin method with sinc functions

In this paper, the sinc-Galerkin method is used for numerically solving a class of nonlinear differential equations with boundary conditions. The importance of this study is that sinc approximation of the nonlinear term is stated as a new theorem. The method introduced here is tested on some nonlinear problems and is shown to be a very efficient and powerful tool for obtaining approximate solutions of nonlinear ordinary differential equations.

Numerical Algorithm of the Fractional Diffusion Equation Based on Sinc-Chebyshev Collocation

Fractional diffusion equations have recently been applied in various area of engineering. In this paper, a new numerical algorithm for solving the fractional diffusion equations with a variable coefficient is proposed. Based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized respectively, the problem is reduced to the solution of a system of linear algebraic equations. The procedure is tested and the efficiency of the proposed algorithm is confirmed through the numerical example.