Using triangular orthogonal functions for solving Fredholm integral equations of the second kind

Babolian, E.; Marzban, Hamid Reza; Salmani, Mohammad Hassan

doi:10.1016/j.amc.2007.12.034

Cited by 34 publications

(17 citation statements)

References 6 publications

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“…(14) we determine N. Then we choose an arbitrary number for k depending on the problem and we choose m, using Eq. (15). We evaluate the results for two consecutive k for different t in [0, t f ) until the results are similar up to a required number of decimal places.…”

Section: Approximation Using Triangular Functionsmentioning

confidence: 99%

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Analysis of time-varying delay systems via triangular functions

Hoseini

Marzban

2011

Applied Mathematics and Computation

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Section: Approximation Using Triangular Functionsmentioning

confidence: 99%

“…The advantage of TF is that unlike BPF, the TF representation does not need any integration to evaluate the coefficients, thereby reducing a lot of computational burden. TF approximation has been successfully used to analysis of dynamic systems [12], variational problems [14], integral equations [15] and integrodifferential equations [16].…”

Section: Introductionmentioning

confidence: 99%

Analysis of time-varying delay systems via triangular functions

Hoseini

Marzban

2011

Applied Mathematics and Computation

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“…in which I is m×m identity matrix, for more details see [27]. We propose a numerical method based on TFs to obtain the solution of Fredholm integral equation and the coupled system of Fredholm integral equation.…”

Section: Multiplication Of Tfsmentioning

confidence: 99%

“…In (27) where f (t) = e t − 1, k(t, s) = s and the exact solution isy(t) = e t . by using TF method, the problem can be solved, for m = 4 and 32 are listed in tables 1 and 2 clearly compares estimation of the solution obtained via TF method by the direct method using maple and a finite iterative algorithm.…”

Section: Illustrative Numerical Examplesmentioning

confidence: 99%

An efficient hybrid method for solving fredholm integral equations using triangular functions

Ali¹,

Ramadan²

2017

ntmsci

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Abstract:In this paper the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations. The obtained system is a variant of coupled Sylvester matrix equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of approximate solution of the unknown functions of the integral problems. Some numerical examples are solved to illustrate the accuracy and the efficiency of the proposed hybrid method. The obtained numerical results are compared with other numerical methods and the exact solutions.

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“…These problems have application in mathematics, physics, and engineering. Recently, using polynomials have been common to solve these equations, see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

2016

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In this paper, we present a direct computational method to solve Volterra integral equations. The proposed method is a direct method based on approximate functions with the Bernstein Multiscaling polynomials. In this method, using operational matrices, the integral equation turns into a system of equations. Our approach can solve nonlinear integral equations of the first kind and the second kind with piecewise solution. The computed operational matrices in this article are exact and new. The comparison of obtained solutions with the exact solutions shows that this method is acceptable. We also compared our approach with two direct and expansion-iterative methods based on the block-pulse functions. Our method produces a system, which is more economical, and the solutions are more accurate. Moreover, the stability of the proposed method is studied and analyzed by examining the noise effect on the data function. The appropriateness of noisy solutions with the amount of noise approves that the method is stable.

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Using triangular orthogonal functions for solving Fredholm integral equations of the second kind

Cited by 34 publications

References 6 publications

Analysis of time-varying delay systems via triangular functions

Analysis of time-varying delay systems via triangular functions

An efficient hybrid method for solving fredholm integral equations using triangular functions

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

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