Using direct method for solving variational problems via triangular orthogonal functions

Babolian, E.; Mokhtari, Reza; Salmani, Mohammad Hassan

doi:10.1016/j.amc.2007.02.080

Cited by 15 publications

(9 citation statements)

References 8 publications

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“…Furthermore, first by using Eq. (14) we determine N. Then we choose an arbitrary number for k depending on the problem and we choose m, using Eq. (15).…”

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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“…Furthermore, first by using Eq. (14) we determine N. Then we choose an arbitrary number for k depending on the problem and we choose m, using Eq. (15).…”

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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“…These functions have been applied for solving variational problems by Babolian et al [10]. In this article, we present new vector forms of triangular functions (TFs), operational matrix of integration, expansion of functions of one and two variables with respect to triangular functions, and other TFs properties.…”

Section: Introductionmentioning

confidence: 98%

Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions

Babolian

Masouri

Hatamzadeh-Varmazyar

2009

Computers & Mathematics with Applications

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a b s t r a c tAn effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

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“…Triangular functions have been introuduced by Deb et al [23] and studied and used by Babolian et al [24]. In this section, definitions of vector forms of TFs vector forms and their properties proposed by Babolian et al [25] are reviewed.…”

Section: Review Of Orthogonal Triangular Functionsmentioning

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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Using direct method for solving variational problems via triangular orthogonal functions

Cited by 15 publications

References 8 publications

Analysis of time-varying delay systems via triangular functions

Analysis of time-varying delay systems via triangular functions

Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions

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

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