Abstract: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 th… Show more
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