Numerical Solution of Non-stationary Problems with a Rational Approximation for Fractional Powers of the Operator

Abstract

AbstractThe numerical solutions of the Cauchy problems for a first and second-order differential-operator equations are discussed. The equation of the problem includes the fractional power of a self-adjoint positive operator. In computational practice, rational approximations of the fractional power operator are widely used. In this work, we construct special time approximations with fractional power operators: the transition to a new level in time provides a set of standard problems for the operator and not for the fractional power operator. Our approach utilizes stable splitting schemes with weights parameters for the additive representation of the rational approximation for the fractional power operator.KeywordsFractional powers of the operatorRational approximationDifferential-operator equationSplitting scheme