‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stab...

In this paper, the numerical solution of nonlinear Fredholm integral equations of second kind is considered by Sinc method. This numerical method combines a discrete Sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the method. So far approximate solutions with polynomial convergence have been report...

Nonlinear parabolic equations; Singularly perturbed equations; Sinc collocation method; Convergence analysis Abstract We propose a numerical method for solving singularly perturbed one-dimensional nonlinear parabolic problems. The equation converted to the nonlinear ordinary differential equation by discretization first in time then subsequently in each time level we use the Sinc collocation me...

EEorts to develop sinc domain decomposition methods for second-order two-point boundary-value problems have been successful, thus warranting further development of these methods. A logical rst step is to thoroughly investigate the extension of these methods to Poisson's equation posed on a rectangle. The Sinc-Galerkin and sinc-collocation methods are, for appropriate weight choices, identical f...

Computation of the Schrodinger equation energy levels is very important in physics. For example we can use these levels to calculate the absorption coefficient and light refraction in a material as well as calculation of the interband and intersubband transition energies. Density of states of the system can also be obtained by using the energy levels. Thereafter we can determine that the system...

We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The is collocation which utilizes Poly-Sinc interpolation to reach preset level accuracy the approximation. Our work extends function approximation, we derived an priori error estimate our and showed its exponential convergence in number iterations. In this work, show iterations...