Bakirova E. A.
Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations
Ukr. Mat. Zh. - 2019. - 71, № 9. - pp. 1176-1191
We propose a numerical method for the solution of linear boundary-value problem for system of integrodifferential equations. This method is based on the approximation of the integral term by a cubic spline and reduction of the original problem to a linear boundary-value problem for a system of loaded differential equations. We also propose new algorithms for finding the numerical solution and a method for the construction of approximate solution to the approximating boundary-value problem.
On the unique solvability of a nonlocal boundary-value problem for systems of loaded hyperbolic equations with impulsive actions
Ukr. Mat. Zh. - 2017. - 69, № 8. - pp. 1011-1029
We consider a nonlocal boundary-value problem with impulsive actions for a system of loaded hyperbolic equations and establish the relationship between the unique solvability of this problem and the unique solvability of a family of two-point boundary-value problems with impulse actions for the system of the loaded ordinary differential equations by method of introduction of additional functions. Sufficient conditions are obtained for the existence of a unique solution to a family two-point boundary-value problems with impulsive effects for the system of loaded ordinary differential equations by using method of parametrization. The algorithms of finding the solutions are constructed. The conditions of unique solvability of the nonlocal boundary-value problem for a system of loaded hyperbolic equations with impulsive actions are established. The numerical realization of the algorithms of the method of parametrization is proposed for the solution of the family of two-point boundary-value problems with impulsive actions for the system of the loaded ordinary differential equations. The results are illustrated by specific examples.