In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. application of proposed leads equation to system algebraic equations that are easy solve. Some examples presented and compared with some methods in literature illustrate ability technique. results demonstrate more efficient, convergent, accurate exa...

Abstract We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2Ψ ∂x2 = βΨ(1 − Ψδ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation met...

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ∆ ~ N + λ~ ∇(~ ∇ · ~ N) = ~ S with λ 6= −1. The source can extend in all the Euclidean space R, provided it decays at least as r−3 (scalar case) or r−4 (vectorial case). A multi-domain app...

The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...

We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for al...