Vasylyk V. Methods without accuracy saturation for differential equations in a Banach space with unbounded operator coefficients

Methods without accuracy saturation of the approximate solution to problems for equations with unbounded operator coefficients in a Banach space are developed. Both classical statements of initial boundary-value problems and problems with nonlocal conditions are considered. In particular, approximate methods for initial problems for an inhomogeneous equation of the first order with constant and variable operator coefficients and problems with multipoint and integral nonlocal conditions are constructed. Numerical methods for second-order equations with operator coefficients are constructed, in particular for a strongly damped hyperbolic equation with initial condition and for an elliptic equation with boundary condition. For equations of elliptic type, numerical methods with multipoint and integral nonlocal conditions are constructed.