The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the SL(2, R) group. In the case of (2j + 1)-dimensional nonunitary representations of that group, 0 < 2j ∈ Z, they are transformed into equations for spin-j fields. A local gauge symmetry associated to the vector system of e...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

The issue of the ”eternal return” is examined from the perspective of the topology of spacetime. Constraints on dynamical laws for the periodic evolution of a system or universe are highlighted. Using a Fourier series expansion, an infinite set of simultaneous linear equations is formulated for the periodic evolution of a system/universe. PACS: 05.70.-a, 05.90.+m, 04.20.Jb, 04.20.Gz

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...

In the literature, several numerical methods are proposed for solvingnth-order fuzzy linear differential equations. However, till now there areonly two analytical methods for the same. In this paper, the fuzzy Kolmogorov'sdifferential equations, obtained with the help of fuzzy Markov modelof piston manufacturing system, are solved by one of these analytical methodsand illustrated that the obtai...

Let Rn,d be the ring of invariants of d-tuples of n × n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters of R3,3 are determined. Homogeneous systems of parameters of R3,2, R4,2 are also pointed out.