Odd degree splines of higher order

Mathur, K. K.; Saxena, Anjula

doi:10.1007/bf01874647

Cited by 4 publications

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“…We have 8/3 A n-2 = -8A n-1 + h 3 [-40/9 f (4) ( 1 ) + 2/9 f (4) ( 2 ) -2/3 f (4) ( 3 ) + 4/3 f (4) ( 4 ) + 32/9 f (4)…”

Section: Using Taylor Expansion For the Function F And Its Derivativementioning

confidence: 99%

Lacunary Interpolation at Odd and Even Nodes

Singh¹,

Pandey²

2016

IJCA

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Here a special (0, 2; 0, 3) lacunary interpolation scheme is considered where the data are prescribed unevenly at even and odd nodes of an arbitrarily defined partition of the unit interval I =[0,1].The problem described as, we have the function values and second derivatives at odd nodes, whereas function values and the thirdderivatives ateven nodes are known, weproved that there existsa unique quantic spline of continuity class C 2 by solving the above mentioned interpolation scheme.Furthermore, it is also proved that this spline function converges to the given function with the desired order of accuracy.

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“…We have 8/3 A n-2 = -8A n-1 + h 3 [-40/9 f (4) ( 1 ) + 2/9 f (4) ( 2 ) -2/3 f (4) ( 3 ) + 4/3 f (4) ( 4 ) + 32/9 f (4)…”

Section: Using Taylor Expansion For the Function F And Its Derivativementioning

confidence: 99%

Lacunary Interpolation at Odd and Even Nodes

Singh¹,

Pandey²

2016

IJCA

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“…In the past this class of splines is used by various authors with different interpolatory conditions, see [6] and [12]. For more related work one can refer [3] - [13]. In this present paper we study the problem in a different perspective where the first derivative of f is given at intermediate points between the nodes and the first derivative of f is known at all the nodes, the theorem states as:…”

Section: Introductionmentioning

confidence: 99%

Using a Quartic Spline Function for Certain Birkhoff Interpolation Problem

Singh¹,

Pandey²

2014

IJCA

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Let f be a real valued function defined in [0, 1], with values known at intermediate points such that the first derivatives of f at all nodes are also known at intermediate points.In this paper, we construct an interpolatory quartic spline s which interpolates the function f. Unique existence and convergence of this spline are also established. This type of construction is known to have found aesthetic utility in finding areas under or bounded by polynomial curves.

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“…The subject was of particular interest to the Hungarian school of mathematicians led by Turgn. Many of them obtained important results about existence, uniqueness, explicit representation and convergence of such interpolatory polynomials when the nodes of interpolation and the knots of the spline coincide [5,6,7,13,17,18,21,22].Others have constructed lacunary deficient splines when the interpolation data is prescribed at points midway between the knots [2,10,11,12,14,15,19,25,26]• A number of papers have also shown the importance of this type of splines in numerical quadratures or in the approximate solution of differential equations [1,3,4,8,9,16,20].The basic aim of this paper is to construct and study quintic lacunary interpolatory splines that match the given values of a function f E C 5 and its second or first derivative at the equidistant knots and whose fourth derivatives interpolate f(4) midway between the knots. Such spline functions may be used to obtain approximate solutions of non-linear differential equations of the fourth order with boundary conditions that arise in the theory of bending and twisting of elastic beams and plates (see, for instance, [23,24]).…”

mentioning

confidence: 99%

“…Others have constructed lacunary deficient splines when the interpolation data is prescribed at points midway between the knots [2,10,11,12,14,15,19,25,26]• A number of papers have also shown the importance of this type of splines in numerical quadratures or in the approximate solution of differential equations [1,3,4,8,9,16,20].…”

mentioning

confidence: 99%

Quintic spline interpolation on uniform meshes

Pittaluga

Sacripante

1996

Acta Math Hung

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1. Introduction. In a series of papers, several authors have studied and solved the problem of lacunary interpolation by splines. The subject was of particular interest to the Hungarian school of mathematicians led by Turgn. Many of them obtained important results about existence, uniqueness, explicit representation and convergence of such interpolatory polynomials when the nodes of interpolation and the knots of the spline coincide [5,6,7,13,17,18,21,22].Others have constructed lacunary deficient splines when the interpolation data is prescribed at points midway between the knots [2,10,11,12,14,15,19,25,26]• A number of papers have also shown the importance of this type of splines in numerical quadratures or in the approximate solution of differential equations [1,3,4,8,9,16,20].The basic aim of this paper is to construct and study quintic lacunary interpolatory splines that match the given values of a function f E C 5 and its second or first derivative at the equidistant knots and whose fourth derivatives interpolate f(4) midway between the knots. Such spline functions may be used to obtain approximate solutions of non-linear differential equations of the fourth order with boundary conditions that arise in the theory of bending and twisting of elastic beams and plates (see, for instance, [23,24]).

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Odd degree splines of higher order

Cited by 4 publications

References 1 publication

Lacunary Interpolation at Odd and Even Nodes

Lacunary Interpolation at Odd and Even Nodes

Using a Quartic Spline Function for Certain Birkhoff Interpolation Problem

Quintic spline interpolation on uniform meshes

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