On approximation by splines of solution of boundary problem

S.G. Dronov (Dnipropetrovsk State University)


For the boundary problem
$$y'' + p(x) y' + q(x) y = r(x), \; y(a) = Y_a, \; y(b) = Y_b$$
we give the approximate solution method of fourth order of accuracy in the form of cubic spline. For truncated problem ($$$p(x) \equiv 0$$$) we establish the prior estimates of error.


Korneichuk N.P. Splines in approximation theory, Nauka, 1984. (in Russian)

Korneichuk N.P. Extremum problems in approximation theory, 1976. (in Russian)

Stechkin S.B., Subbotin Yu.N. Splines in computational mathematics, 1976. (in Russian)

Zavialov Yu.S., Kvasov B.I., Miroshnichenko V.L. Methods of spline-functions, 1980. (in Russian)

Marchuk G.I., Shaidurov V.V. Increasing the accuracy of solutions of difference schemes, 1979. (in Russian)

Dronov S.G., Ligun A.A. "On one spline-method of solving boundary problem", Ukrainian Math. J., 1987; 41(5): pp. 703-707. (in Russian) doi:10.1007/BF01060554

DOI: https://doi.org/10.15421/248706



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