in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

Soil spectroscopy has shown to be a fast, cost-effective, environmentally friendly, non-destructive, reproducible and repeatable analytical technique. Soil components, as well as types of instruments, protocols, sampling methods, sample preparation, spectral acquisition techniques and analytical algorithms have a combined influence on the final performance. Therefore, it is important to charact...

This paper is concerned with the numerical solution of Volterra integral equations third kind non-smooth solutions based on recursive approach spectral Tau method. To this end, a new set fractional version canonical basis polynomials (called FC-polynomials) introduced. The approximate polynomial Tau-solution) expressed in terms FC-polynomials. structure Tau-solution allows recovering standard d...

We consider a diierent approach for the Chebyshev-tau spectral method by a modiication of the basis for the test function space. This leads to sparse matrices, which are better conditioned than those generated by the usual method, as being pointed out by some numerical examples.

Aims. We obtain accurate estimates for the individual masses of the components of the tight binary system T Tau S to settle the ongoing debate on the nature of T Tau Sa, a so-called infrared companion. Methods. We take advantage of the fact that T Tau S belongs to a triple system composed of two hierarchical orbits to simultaneously analyze the motion of T Tau Sb in the rest frames of T Tau Sa ...

For the known spectral methods (Galerkin, Tau, Collocation) the condition number behaves like 0(N4) (N: maximal degree of polynomials). We introduce a spectral method with an 0(N2) condition number. The advantages with respect to propagation of rounding errors and preconditioning are demonstrated. A direct solver for constant coefficient problems is given. Extensions to variable coefficient pro...

In this article, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With aid of new semi-norm equivalence between method finite difference method, prior bound numerical solution in discrete L ∞ $$ {L}^{\infty } -norm is obtained from momentum conservation law. Subsequently, based on energy solution, show that, wit...

Here, in this article, we investigate the solution of a general family fractional-order differential equations by using spectral Tau method sense Liouville–Caputo type fractional derivatives with linear functional argument. We use Chebyshev polynomials second kind to develop recurrence relation subjected certain initial condition. The behavior approximate series solutions are tabulated and plot...