Fuzzy transforms (or F-transforms for short) are an approximation technique recently introduced. The main application is referred to image and data compression. There are really few works devoted t...

An alternative use of fuzzy transform with application to a class of delay differential equations

Modified Chebyshev collocation method for pantograph-type differential equations

The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem into a continuous-time optimization problem and then utilize a transferred Legendre pseudospectral method to discretize the problem. By solving this discrete problem, we can attain the pointwise and continuous estimated solutions for the major pantograph delay differential equation. The convergence of method has been considered. Also, numerical experiments are described to show the performance and precision of the presented technique. Moreover, the obtained results are compared with those from other techniques.

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A new numerical method to solve pantograph delay differential equations with convergence analysis

This paper investigates the stability of the numerical solutions of general lin- ear methods for a class of nonlinear neutral delay differential equations.It is shown that (k,p,0)-algebraically stable general linear methods,under some restrictions,preserves the analogous stability of the original differential equations.In particular,it is proven that all algebraically stable general linear methods with restricted mesh can preserve the stability of the underlying systems without conditions.

Nonlinear Stability of General Linear Methods for Neutral Delay Differential Equations

Extended block boundary value methods for neutral equations with piecewise constant argument

In this paper, for the neutral equations with piecewise continuous argument, we construct a spectral collocation method by combining the shifted Legendre–Gauss–Radau interpolation and a multi-domai...

A multi-domain Legendre spectral collocation method for nonlinear neutral equations with piecewise continuous argument

This paper is concerned with the long-time behaviour of the numerical solutions to a class of linear non-autonomous neutral delay differential equation with proportional delays. Our purpose is to give some asymptotic estimates of the θ-methods with constant stepsize discretization and formulate their upper bounds. Asymptotic estimate not only describes more accurate than asymptotic stability, but also gives an upper bound estimate of the solution for the long-time behaviour. We also compare the known results and show that our formulae improve and generalize these results. Some numerical examples are given in the end of this paper to confirm the theoretical results.

Wansheng Wang

Papers

A multi-domain Legendre spectral collocation method for nonlinear neutral equations with piecewise continuous argument

The asymptotic behaviour of the θ-methods with constant stepsize for the generalized pantograph equation