A numerical method for solving the Cauchy problem for ODEs using a system of polynomials generated by a system of modified Laguerre polynomials

In this paper, we consider a numerical realization of an iterative method for solving the Cauchy problem for ordinary differential equations, based on representing the solution in the form of a Fourier series by the system of polynomials $\{L_{1,n}(x;b)\}_{n=0}^\infty$, orthonormal with respect to the Sobolev-type inner product $$ \langle f,g\rangle=f(0)g(0)+\int_{0}^\infty f'(x)g'(x)\rho(x;b)dx $$ and generated by the system of modified Laguerre polynomials $\{L_{n}(x;b)\}_{n=0}^\infty$, where $b>0$. In the approximate calculation of the Fourier coefficients of the desired solution, the Gauss -- Laguerre quadrature formula is used.

CALCULATING THE RIGHT-EIGENVECTORS OF A SPECIAL VIBRATION CHAIN BY MEANS OF MODIFIED LAGUERRE POLYNOMIALS

This contribution deals with the identification of the right-eigenvectors of a linear vibration system with arbitrary n degrees of freedom as given in [1]. Applying the special distribution of stiffnesses and masses given in [1] yields a remarkable sequence of matrices for arbi- trary n. For computing the (right-)eigenvectors a generalised approach allowing the use of Laguerre polynomials is performed.