We investigate the existence of a solution of a boundary problem for linear integro-differential equations, give a calculus scheme for an approximate solution of the boundary problem by means of $B$-splines and study its convergence conditions.
[1] Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. Methods of spline functions. - M.: Nauka, 1980. - 350 p.
[2] Ahlberg J., Nelson E., Walley J. Spline Theory and Its Applications. - M.: Mir, 1972. - 316 p.
[3] Loscalzo F. R., Talbot T.D. Spline function approximations for solutions of ordinary differential equations // SIAM J. Numer. Anal. - 1967. - V.4, N3. - 1967. - P. 433-445.
[4] Samoylenko A.M., Ronto N.I. Numerical and analytical methods for studying solutions to boundary value problems. - K.: Nauk. dumka, 1985. - 224 p.
[5] Samoylenko A.M., Laptinsky V.N., Kenzhebaev K.K. Constructive methods for studying periodic and multipoint boundary value problems. - K.: Institute of Mathematics of the National Academy of Sciences of Ukraine, 1999. - 220 p.
[6] Hartman F. Ordinary differential equations. - M.: Mir, 1970. - 684 p.
[7] Cherevko I.M., Yakimov I.V. Numerical method for solving boundary value problems for integro-differential equations with argument / / Ukr. mat. zhurn. - 1989. - V.41, № 6. - P. 854-860.
- ACS Style
- Nastasy , O.B.; Cherevko, I.M. Solving linear boundary value problems for integro-differential equations using the spline collocation method. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Nastasy OB, Cherevko IM. Solving linear boundary value problems for integro-differential equations using the spline collocation method. Bukovinian Mathematical Journal. 2018; 1(454).
- Chicago/Turabian Style
- O. B. Nastasy , Igor Mykhailovych Cherevko. 2018. "Solving linear boundary value problems for integro-differential equations using the spline collocation method". Bukovinian Mathematical Journal. 1 no. 454.