Integro quintic splines and their approximation properties

Жанлав, Т.; Mijiddorj, Renchin-Ochir

doi:10.1016/j.amc.2014.01.043

Cited by 9 publications

(24 citation statements)

References 6 publications

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“…In fact, the inner approximation errors are mainly determined by the given n integral values in (2), while the boundary errors are mainly effected by the artificial end conditions. It is checked that our inner errors of y 1 in Tables 2-6 are similar to the ones in [2,14,18], which are obtained by using five or seven additional exact end conditions. It shows that our new method can obtain satisfactory approximation results by using fewer data than the methods in [2,14,18].…”

Section: Numerical Testsmentioning

confidence: 95%

“…In the next section, (7)- (9), (11) and (15) will be used as the artificial end conditions for integro interpolation; see (18) and (19).…”

Section: Artificial End Conditionsmentioning

confidence: 99%

“…In this paper, we will mainly focus on the quintic spline methods; see [2,14,[17][18][19] for the existing ones.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, besides the integral values (2), the method must use seven additional exact end conditions in terms of y(x 0 ), y (x 0 ), y (x 1 ), y (x n−1 ), y (x n ), y (x 0 ) and y (x n ). Later, a new algorithm was given in [18] to simplify the construction of integro quintic spline. It mainly required solving two linear three-diagonal systems.…”

Section: Introductionmentioning

confidence: 99%

“…The problem arises in many fields, such as numerical analysis, mathematical statistics, environmental science, mechanics, electricity, climatology, oceanography, and so on. We refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for its applied backgrounds and some recent developments.…”

Section: Introductionmentioning

confidence: 99%

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A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Lang

2017

Algorithms

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Abstract:In this paper, to overcome the innate drawbacks of some old methods, we present a new quintic spline method for integro interpolation. The method is free of any exact end conditions, and it can reconstruct a function and its first order to fifth order derivatives with high accuracy by only using the given integral values of the original function. The approximation properties of the obtained integro quintic spline are well studied and examined. The theoretical analysis and the numerical tests show that the new method is very effective for integro interpolation.

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Section: Numerical Testsmentioning

confidence: 95%

“…In the next section, (7)- (9), (11) and (15) will be used as the artificial end conditions for integro interpolation; see (18) and (19).…”

Section: Artificial End Conditionsmentioning

confidence: 99%

“…In this paper, we will mainly focus on the quintic spline methods; see [2,14,[17][18][19] for the existing ones.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Lang

2017

Algorithms

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Uniform algebraic hyperbolic spline quasi‐interpolant based on mean integral values

Barrera

Eddargani

Lamnii

2020

Comp and Math Methods

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In the present work, a novel spline quasi-interpolation operator reproducing both constant polynomials and algebraic hyperbolic functions is presented. The quasi-interpolant to a given function is defined from the integrals on every interval of the function to be approximated. Compared to the other existing methods, this operator does not need any additional end conditions and it is easy to be implemented without solving any system of equations. The approximation properties of the operator are theoretically analyzed and some numerical tests are presented to illustrate its performance.

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On algebraic trigonometric integro splines

Eddargani

Lamnii

2019

Z Angew Math Mech

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In this paper, we present a new kind of quadratic approximation operator reproducing of both algebraic and trigonometric functions. It is called integro quadratic splines interpolant, which agree with the given integral values of a univariate real-valued function over the same intervals, rather than the functional values at the knots. Efficient approximations of fractional integrals and fractional Caputo derivatives based on this interpolant, are constructed and well studied. The general approximation error is studied too, and the super convergence property is also derived when the interval is equally partitioned. Numerical examples illustrate that our method is very effective and our quadratic algebraic trigonometric integro spline has higher approximation ability than others. K E Y W O R D Salgebraic trigonometric splines, error bound, fractional caputo derivatives, fractional integrals, integro spline quasi-interpolant

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Integro quintic splines and their approximation properties

Cited by 9 publications

References 6 publications

A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Uniform algebraic hyperbolic spline quasi‐interpolant based on mean integral values

On algebraic trigonometric integro splines

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