Volodymyr L. Makarov

Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces

New exponentially convergent algorithms for the operator exponential generated by a strongly positive operator

Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces

A

Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems

in a Banach space

A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes

X

Difference schemes for nonlinear BVPs on the half-axis

are proposed. These algorithms are based on representations by a Dunford--Cauchy integral along paths enveloping the spectrum of

Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers

A

The FD-method for solving Sturm-Liouville problems with special singular differential operator

combined with a proper quadrature involving a short sum of resolvents where the choice of the integration path dramatically affects desired features of the algorithms. A parabola and a hyperbola are analyzed as the integration paths, and scales of estimates of dependence on the smoothness of initial data, i.e., of the initial vector and of the inhomogeneous right-hand side, are obtained. One of the algorithms possesses an exponential convergence rate for the operator exponential

Exponentially convergent algorithms for abstract differential equations

e^{-At}

Exponentially Convergent Method for the m-Point Nonlocal Problem for a First Order Differential Equation in Banach Space

for all

A numerical-analytic method for solving the Cauchy problem for ordinary differential equations

t\ge 0