A Special Quintic Spline for (0,1,4) Lacunary Interpolation and Cauchy Initial Value Problem


Kulbhushan Singh,




Cauchy Initial Value Problem,Lacunary Interpolation,Spline function,


In the present paper a special lacunary interpolation problem is solved in which function value, first derivatives and fourth derivatives are prescribed at nodes of the unit interval I = [0, 1]. A special spline function is obtained for it. Then the theorem of unique existence and convergence for this spline function are proved. In our next communication we will show that this special function can be used to solve Cauchy’s Initial value problem.


I Ambrish Kumar Pandey,Q S Ahmad,Kulbhushan Singh, “Lacunary
Interpolation (0,2;3) Problem and Some Comparison from Quartic Splines”,
American J. of App. Math. and Statistics, 2013, Vol. 1, No. 6, 117-120.
II Fawzy, T.,Spline functions and the Cauchy’s problem II, Acta Math. Hung. 29
(3-4) 1977,259-271.
III Gyorvari,.J., Lakunare spline funktionun das Cauchy problem, Acta Math
Hung., 44 (3-4). 1984, 327-335.
IV K. B. Singh, Ambrish Kumar Pandey and Qazi Shoeb Ahmad,“Solution of a
Birkhoff Interpolation Problem by a Special Spline Function”, International J.
of Comp. App., Vol.48, 22-27,June 2012.

V Loscalzo, F.R. and Talbot, T. D., Spline and approximation for solutions of
ordinary differential equations, SIAM J. Numer. Anal. Vol. 4, 1967, 433-445.
VI Micula, Gh., Approximate solution of the differential equation y” (x) = f(x,y)
with spline functions, Math. ofcomput. 27 (1973), 807-816.
VII Sallam, S. and Hussain, M. A.,deficient spline for approximation to second
order differential equations, Appl. Math Modeling, Vol.8, 1984, 408-412.

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