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Information × Registration Number 0201U001441, 0199U002126 , R & D reports Title Functional-discrete methods of the high rate of accuracy for solving the problems of the mathematical physics popup.stage_title Head Makarov V. L., Registration Date 05-02-2001 Organization Institute of mathematics NAS of Ukraine popup.description2 The goal of the research is a creation of the new high-precision methods for computation of some problems in mathematical physics, such as Sturm-Liuville, abstract equations in Hilbert and Banach spaces, sloshing in the rectangular tanks. The constructive sufficient conditions for the Sturm-Liuville problem with two-point separated and periodical boundary conditions have been found. The conditions provide a convergence of the FD-method that is not slower than the according convergence of geometric progression with a denominator. The denominator depends on parameter of discretization directly proportional and on number of correspondent eigenvalue inversely. The estimate of convergence rate for the Fourier-Tchebyshov series technique for an abstract non-homogeneous linear first order equation has been improved. The constructive representations of solutions of abstract problems for the first-order hyperbolic differential equation in Hilbert space based on FD-method have been found. Using these constructiv e representations it was built and proved some numerical algorithms. It was estimated an accuracy of approximate solutions. The sufficient r-stability conditions in Banach space for three-layer schemes with unbounded operator coefficient have been found. The theorems about solvability sufficient conditions of polynomial operator interpolation have been proved. The numerical analytical method for approximation of the operator exponent with strongly P-positive generator in Banach space, and an exponential convergence rate has been constructed. The method can be parallelized. The error estimates of full discrete approximation of the numerical-analytical method of sloshing in tanks with structural inclusions have been found and ground. Keywords: Sturm-Liuville problem, FD-method, operator exponent, strongly P-positive operator, r-stability, sloshing, Cayley transform. Product Description popup.authors popup.nrat_date 2020-04-02 Close