Direct Walsh-wavelet packet method for variational problems

Glabisz, W.

doi:10.1016/j.amc.2003.11.002

Cited by 14 publications

(4 citation statements)

References 10 publications

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“…Typical examples are the Walsh functions [22,23], block pulse functions [24][25][26][27], Legendre polynomials [28][29][30], Chebyshev polynomials [31], Laguerre polynomials [32,33], and Fourier series [34,35].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

Sun

2011

Computers & Mathematics with Applications

143

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a b s t r a c tThe Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.Crown

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Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

Sun

2011

Computers & Mathematics with Applications

143

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“…Several methods have been used to solve variational problems in the literature (cf. , [4][5][6][7][8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function

Bataineh

2018

Filomat

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In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of variational problems. The operational matrix of differentiation is introduced and utilized to reduce the calculus of variations problems to the solution of system of algebraic equations. The solutions are obtained in the form of rapidly convergent finite series with easily computable terms. Comparison between the present method and the homotopy perturbation method (HPM), the non-polynomial spline method and the B-spline collocation method are made to show the effectiveness and efficiency for obtaining approximate solutions of the calculus of variations problems. Moreover, convergence analysis based on residual function is investigated to verified the numerical results.

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“…In addition, HTOMs have not only simple operations such as addition and subtraction but also fast algorithm, which leads to that HTOMs have so small calculation quantity that they are very suitable for the real time application. Moreover, only varying any one of two parameters s and r in the same program, different HTOMs can be easily obtained, which is very convenient in the practical application [9][10][11][12]. * Corresponding authors.…”

Section: Introductionmentioning

confidence: 99%