Komashinskaya I. V.
Numerical solutions of fractional system, two-point BVPs using iterative reproducing kernel algorithm
Ukr. Mat. Zh. - 2018. - 70, № 5. - pp. 599-610
We propose an efficient computational method, namely, the iterative reproducing kernel method for the approximate solution of fractional-order systems of two-point time boundary-value problems in the Caputo sense. Two extended inner-product spaces are constructed in which the boundary conditions of the systems are satisfied. The reproducing kernel functions are constructed to get an accurate algorithm for the investigation of fractional systems. The developed procedure is based on generating the orthonormal basis with an aim to formulate the solution throughout the evolution of the algorithm. The analytic solution is represented in the form of a series in the reproducing kernel Hilbert space with readily computed components. In this connection, some numerical examples are presented to show the good performance and applicability of the developed algorithm. The numerical results indicate that the proposed algorithm is a powerful tool for the solution of fractional models arising in different fields of sciences and engineering.
Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1182–1185
We establish conditions for the existence and uniqueness of a solution of a quasilinear mixed problem for a quasiwave equation.