<p style='text-indent:20px;'>In present work, a step-by-step Legendre collocation method is employed to solve class of nonlinear fractional stochastic delay differential equations (FSDDEs). The converts the FSDDE into non-delay equation (FSDE). Then, approach considered obtain numerical solution in each step. By using scheme, FSDE reduced system. Moreover, error analysis this investigated...

This work deals with the H1 condition numbers and the distribution of the ~ N;Msingular values of the preconditioned operators f~ 1 N;M WN;M ÂN;Mg. ÂN;M is the matrix representation of the Legendre Spectral Collocation discretization of the elliptic operator A de ned by Au := u + a1ux + a2uy + a0u in (the unit square) with boundary conditions: u = 0 on 0; @u @ A = u on 1. ~ N;M is the sti ness ...

Solutions of partial differential equations with coordinate singularities often have special behavior near the singularities, which forces them to be smooth. Special treatment for these coordinate singularities is necessary in spectral approximations in order to avoid degradation of accuracy and efficiency. It has been observed numerically in the past that, for a scheme to attain high accuracy,...

Fractional derivative models involving generalized Mittag-Leffler kernels and opposing are investigated. We first replace the classical with GMLK in order to obtain new fractional-order (GMLK) three parameters that utilize a spectral collocation method based on Legendre’s polynomials for evaluating numerical solutions of pr. then construct scheme by using Legendre polynomials. In model, we dire...

In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version ...

This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable robust vibration analyses. To this end, regression-based polynomial chaos expansion (PCE) is used to track uncertainties, surrogate approach (PSA) developed treat uncertainties. non-intrusive dual-layer framework shares same collocation pool, which extracted fro...

The Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity. The MHD systems are used effectively in many applications including power generators, pumps, accelerators, electrostatic filters, droplet filters, the design of heat exchangers, the cooling of reactors, etc. For the MHD Falkner-Skan equation, we have developed a new numerical technique transforming t...