Regularization of the procedure for inverting the Laplace transform using quadrature formulas

The problem of inversion the integral Laplace transform, which belongs to class ill-posed problems, is considered. Integral equations are reduced ill-conditioned systems linear algebraic (SLAE), in unknowns either expansion coefficients a series terms shifted Legendre polynomials, or approximate values desired original at number points. first step reduction SLAE apply quadrature formulas that provide minimum condition SLAE. Regularization methods used obtain reliable solution system. A common strategy use Tikhonov stabilizer its modifications. variant regularization method for with oscillatory-type matrices presented, significantly reduces conditionality comparison classical scheme. given actually constructing special quadratures leading problems oscillation matrices.