Numerical solution for three-dimensional nonlinear mixed Volterra–Fredholm integral equations via three-dimensional block-pulse functions

Mirzaee, Farshid; Hadadiyan, Elham; Bimesl, Saeed

doi:10.1016/j.amc.2014.03.087

Cited by 18 publications

(19 citation statements)

References 9 publications

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“…(18) where k is number of modifications of the M3D-BFs series. Also, similarly [19], we can show that lim m→+∞ f m,ε i (x, y, z) = f (x, y, z). x, y, z, s, t, r) = k(x, y, z, s, t, r) − k m (x, y, z, s, t, r), (x, y, z, s, t, r) …”

Section: Theorem 2 Assume F(x Y Z) Is Continuous and Is Differentisupporting

confidence: 68%

“…Then we have: ||e m (x, y, z, s, t, r)|| ≤ √ 6 km ||Dk(x, y, z, s, t, r)||, (19) and ||e m (x, y, z, s, t, r)…”

Section: Theorem 3 Suppose That F(x Y Z) Be An Smooth Enough Functmentioning

confidence: 99%

“…The literature on the numerical solution methods of such equations is fairly extensive [2][3][4][5][6][7][8][9]. But the analysis of computational methods for two-dimensional integral equations seem to have been discussed in only a few papers [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Mirzaee

Hadadiyan

2015

Applied Mathematics and Computation

Self Cite

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Section: Theorem 2 Assume F(x Y Z) Is Continuous and Is Differentisupporting

confidence: 68%

“…Then we have: ||e m (x, y, z, s, t, r)|| ≤ √ 6 km ||Dk(x, y, z, s, t, r)||, (19) and ||e m (x, y, z, s, t, r)…”

Section: Theorem 3 Suppose That F(x Y Z) Be An Smooth Enough Functmentioning

confidence: 99%

See 1 more Smart Citation

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Mirzaee

Hadadiyan

2015

Applied Mathematics and Computation

Self Cite

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“…Lin Liu and Hong Zhang applied the single layer regularized meshless method for three-dimensional Laplace problems in [25]. In [26][27][28], the authors utilized the threedimensional block-pulse functions and Jacobi polynomials to obtain the numerical solutions of three-dimensional integral equations. Based on the above research, a numerical technique based three-dimensional block-pulse functions in our study is proposed to solve three-dimensional fractional Poisson type equations with Neumann boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions

Xie

Yao

et al. 2018

Bound Value Probl

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In this paper, a numerical scheme based on the three-dimensional block-pulse functions is proposed to solve the three-dimensional fractional Poisson type equations with Neumann boundary conditions. The differential operational matrices of fractional order of the three-dimensional block-pulse functions are derived from one-dimensional block-pulse functions, which are used to reduce the original problem to solve a system of linear algebra equations. In addition, the convergence analysis of the proposed method is deeply investigated. Lastly, several numerical examples are presented and the numerical results obtained show that our method is effective and feasible.

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“…In the recent years, many researchers studied Volterra integral equation using the differential transform method (DTM) [1,5,6,9]. For three-dimensional integral equations, in [4] the author used the three-dimensional differential transform method and authors in [8] applied the block-pulse functions methods on three-dimensional nonlinear mixed Volterra-Fredholm integral equation. Recently, the differential transform method is modified to the so-called Reduced Differential Transform Method to solve Volterra integral equation [1].…”

Section: Introductionmentioning

confidence: 99%

Solving three-dimensional Volterra integral equation by the reduced differential transform method

Armiti

Suwan

2016

IJAMR

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In this article, the results of two-dimensional reduced differential transform method is extended to three-dimensional case for solving three dimensional Volterra integral equation. Using the described method, the exact solution can be obtained after a few number of iterations. Moreover, examples on both linear and nonlinear Volterra integral equation are carried out to illustrate the efficiency and the accuracy of the presented method.

show abstract

Numerical solution for three-dimensional nonlinear mixed Volterra–Fredholm integral equations via three-dimensional block-pulse functions

Cited by 18 publications

References 9 publications

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions

Solving three-dimensional Volterra integral equation by the reduced differential transform method

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