Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique. (English) Zbl 1484.65342
Summary: A novel numerical technique to solve 2D Fredholm integral equations (2DFIEs) of first kind is proposed in this study. This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence analysis which shows the fast converges of this technique to the actual solution. Some problems of 2D linear Fredholm integral equations are illustrated to show the efficiency of the proposed scheme.
Keywords:
discretization; numerical solution; 2D Fredholm integral equations; 2D Bernstein’s approximation; convergence analysisReferences:
| [1] | J. P. Kauthen, i>Continuous time collocation methods for Volterra-Fredholm integral equations</i, Numeriche Math., 5, 409-424 (1989) · Zbl 0662.65116 |
| [2] | F. Khan; G. Mustafa; M. Omar, t al., <i>Numerical approach based on Bernstein polynomials for</i> <i>solving mixed Volterra-Fredholm integral equations</i, AIP Adv., 7 (2017) |
| [3] | M. M. Mustafa; N. I. Ghanim, i>Numerical solution of linear Volterra-Fredholm integral equations</i> <i>using Lagrange polynomials</i, Math. Theory Model., 4, 158-167 (2014) |
| [4] | A. Alipanah; S. Esmaeili, i>Numerical solution of the two-dimensional Fredholm integral equations</i> <i>using Gaussian radial basis function</i, J. Comput. Appl. Math., 235, 5342-5347 (2011) · Zbl 1226.65105 · doi:10.1016/j.cam.2009.11.053 |
| [5] | C. Heitzinger, A. Hössinger, S. Selberherr, <i>An algorithm for the smoothing three-dimensional</i> <i>monte carlo ion implantation simulation results</i>, Proc. 4th Mathmod Vienna, (2003), 702-711. · Zbl 1106.82325 |
| [6] | A. Fallahzadeh, i>Solution of two-dimensional Fredholm integral equation via RBF-triangular</i> <i>method</i, J. Interpolat. Approx. Sci. Comput., 12 (2012) |
| [7] | F. Khan; M. Omar; Z. Ullah, i>Discretization method for the numerical solution of 2D Volterra</i> <i>integral equation based on two-dimensional Bernstein polynomial</i, AIP Adv., 8 (2018) |
| [8] | F. H. Shekarabi; K. Maleknejad; R. Ezzati, i>Application of two-dimensional Bernstein polynomials</i> <i>for solving mixed Volterra Fredholm integral equations</i, Afr. Mat., 26, 1237-1251 (2015) · Zbl 1327.65043 · doi:10.1007/s13370-014-0283-6 |
| [9] | A. Tari; S. Shahmorad, i>A computational method for solving two-dimensional linear Fredholm</i> <i>integral equations of the second kind</i, ANZIAM J., 49, 543-549 (2008) · Zbl 1154.65100 · doi:10.1017/S1446181108000126 |
| [10] | W. J. Xie; F. R. Lin, i>A fast numerical solution method for two dimensional Fredholm integral</i> <i>equations of the second kind</i, Appl. Numer. Math., 59, 1709-1719 (2009) · Zbl 1169.65128 · doi:10.1016/j.apnum.2009.01.009 |
| [11] | H. Guoqiang; W. Jiong, i>Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm</i> <i>integral equations</i, J. Comput. Appl. Math., 134, 259-268 (2001) · Zbl 0989.65150 · doi:10.1016/S0377-0427(00)00553-7 |
| [12] | X. Wang; R. A. Wildman; D. S. Weile, t al., <i>A finite difference delay modeling approach to the</i> <i>discretization of the time domain integral equations of electromagnetics</i, IEEE Trans. Antennas Propag., 8, 2442-2452 (2008) · Zbl 1369.78846 |
| [13] | T. N. Narasimhan; P. A. Witherspoon, i>An integrated finite difference method for analyzing fluid</i> <i>flow in porous media</i, Water Resorces Res., 12, 57-64 (1976) · doi:10.1029/WR012i001p00057 |
| [14] | M. Jalalvanda; B. Jazbib; M. R. Mokhtarzadehc, i>A finite difference method for the smooth solution</i> <i>of linear volterra integral equations</i, Int. J. Nonlinear Anal. Appl., 2, 1-10 (2013) · Zbl 1284.49047 |
| [15] | A. Khalid; M. N. Naeem; Z. Ullah, t al., <i>Numerical solution of the boundary</i> <i>value problems arising in magnetic fields and cylindrical shells</i, Mathematics, 7 (2019) |
| [16] | S. S. Ray; Om P. Agrawal; R. K. Bera, t al., <i>Analytical and numerical methods for solving partial</i> <i>differential equations and integral equations arising in Physical Models</i, Abstr. Appl. Anal., 14 (2014) |
| [17] | A. Shaikh; A. Tassaddiq; K. S. Nisar, t al., <i>Analysis of differential equations involving CaputoFabrizio fractional operator and its applications to reaction diffusion equations</i, Adv. Difference Equ., 178 (2019) · Zbl 1459.35383 |
| [18] | A. Shaikh; K. S. Nisar, i>Transmission dynamics of fractional order Typhoid fever model using</i> <i>CaputoFabrizio operator</i, Chaos Solitons Fractals, 128, 355-365 (2019) · Zbl 1483.34017 · doi:10.1016/j.chaos.2019.08.012 |
| [19] | M. Khader; K. M. Saad, i>A numerical study using Chebyshev collocation method for a problem</i> <i>of biological invasion: Fractional Fisher equation</i, Int. J. Biomath., 11 (2018) · Zbl 1405.92290 |
| [20] | J. F. Aguiler; K. M. Saad; D. Baleanu, i>Fractional dynamics of an erbium-doped fiber laser model</i, Opt. Quantum Electron., 51 (2019) |
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