In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...

we prove the generalized hyers--ulam stability  of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.

in this paper, we consider non-linear ginsburg-pitaevski-gross equation with the rosen-morse and modifiedwoods-saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. we use the runge- kutta-fehlberg approximation method to solve the resulting non-linear equation.