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Volumn 22, Issue 9, 2016, Pages 2288-2310

A highly accurate collocation algorithm for 1 + 1 and 2 + 1 fractional percolation equations

Author keywords

collocation method; Gauss type quadrature; orthogonal polynomials; Space fractional percolation equations; two dimensional fractional percolation equations

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; GAUSSIAN DISTRIBUTION; POLYNOMIALS; SOLVENTS;

EID: 84968833938     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546315597815     Document Type: Article
Times cited : (32)

References (46)
  • 1
    • 84929170108 scopus 로고    scopus 로고
    • Newblock A method based on Legendre pseudo-spectral approximations for solving inverse problems of parabolic types equations
    • Abdelkawy M, Ahmed EA, Sanchez P, (2015a) newblock A method based on Legendre pseudo-spectral approximations for solving inverse problems of parabolic types equations. Mathematical Sciences Letters 4 (1): 81-90.
    • (2015) Mathematical Sciences Letters , vol.4 , Issue.1 , pp. 81-90
    • Abdelkawy, M.1    Ahmed, E.A.2    Sanchez, P.3
  • 3
    • 84968906237 scopus 로고    scopus 로고
    • An approximate solution for a fractional model of generalized Harry Dym equation
    • Al-Khaled K, Alquran M, (2014) An approximate solution for a fractional model of generalized Harry Dym equation. Mathematical Sciences 8 (4): 125-130.
    • (2014) Mathematical Sciences , vol.8 , Issue.4 , pp. 125-130
    • Al-Khaled, K.1    Alquran, M.2
  • 4
    • 84887174494 scopus 로고    scopus 로고
    • Solving multidimensional FOCPs with inequality constraint by BPs operational matrices
    • Alipour M, Rostamy D, Baleanu D, (2012) Solving multidimensional FOCPs with inequality constraint by BPs operational matrices. Journal of Vibration and Control 19 (16): 2523-2540.
    • (2012) Journal of Vibration and Control , vol.19 , Issue.16 , pp. 2523-2540
    • Alipour, M.1    Rostamy, D.2    Baleanu, D.3
  • 6
    • 84907494463 scopus 로고    scopus 로고
    • An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system
    • Bhrawy A, (2014) An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system. Applied Mathematics and Computation 247: 30-46.
    • (2014) Applied Mathematics and Computation , vol.247 , pp. 30-46
    • Bhrawy, A.1
  • 7
    • 84898537327 scopus 로고    scopus 로고
    • A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
    • Bhrawy A, Doha E, Baleanu D, Ezz-Eldien S, (2015a) A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations. Journal of Computational Physics 293: 142-156.
    • (2015) Journal of Computational Physics , vol.293 , pp. 142-156
    • Bhrawy, A.1    Doha, E.2    Baleanu, D.3    Ezz-Eldien, S.4
  • 8
    • 84919935961 scopus 로고    scopus 로고
    • A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
    • Bhrawy A, Zaky M, (2015a) A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations. Journal of Computational Physics 281: 876-895.
    • (2015) Journal of Computational Physics , vol.281 , pp. 876-895
    • Bhrawy, A.1    Zaky, M.2
  • 9
    • 84925537827 scopus 로고    scopus 로고
    • Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation
    • Bhrawy A, Zaky M, (2015b) Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation. Nonlinear Dynamics 80 (1): 101-116.
    • (2015) Nonlinear Dynamics , vol.80 , Issue.1 , pp. 101-116
    • Bhrawy, A.1    Zaky, M.2
  • 10
    • 84968843712 scopus 로고    scopus 로고
    • Efficient Legendre spectral tau algorithm for solving the two-sided space-time Caputo fractional advection-dispersion equation
    • Epub ahead of print 22 January 2015. DOI: 10.1177/1077546314566835
    • Bhrawy A, Zaky M, Machado JT, (2015b) Efficient Legendre spectral tau algorithm for solving the two-sided space-time Caputo fractional advection-dispersion equation. Journal of Vibration and Control. Epub ahead of print 22 January 2015. DOI: 10.1177/1077546314566835.
    • (2015) Journal of Vibration and Control
    • Bhrawy, A.1    Zaky, M.2    Machado, J.T.3
  • 12
    • 79551635060 scopus 로고    scopus 로고
    • Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term
    • Chen CM, Liu F, Anh V, Turner I, (2011a) Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term. Applied Mathematics and Computation 217 (12): 5729-5742.
    • (2011) Applied Mathematics and Computation , vol.217 , Issue.12 , pp. 5729-5742
    • Chen, C.M.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 13
    • 79952279830 scopus 로고    scopus 로고
    • A novel implicit finite difference method for the one-dimensional fractional percolation equation
    • Chen S, Liu F, Anh V, (2011b) A novel implicit finite difference method for the one-dimensional fractional percolation equation. Numerical Algorithms 56 (4): 517-535.
    • (2011) Numerical Algorithms , vol.56 , Issue.4 , pp. 517-535
    • Chen, S.1    Liu, F.2    Anh, V.3
  • 14
    • 84919836380 scopus 로고    scopus 로고
    • Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media
    • Chen S, Liu F, Burrage K, (2014) Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Computers & Mathematics with Applications 68 (12): 2133-2141.
    • (2014) Computers & Mathematics with Applications , vol.68 , Issue.12 , pp. 2133-2141
    • Chen, S.1    Liu, F.2    Burrage, K.3
  • 15
    • 84870061665 scopus 로고    scopus 로고
    • An implicit numerical method for the two-dimensional fractional percolation equation
    • Chen S, Liu F, Turner I, Anh V, (2013) An implicit numerical method for the two-dimensional fractional percolation equation. Applied Mathematics and Computation 219 (9): 4322-4331.
    • (2013) Applied Mathematics and Computation , vol.219 , Issue.9 , pp. 4322-4331
    • Chen, S.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 17
    • 84959519842 scopus 로고    scopus 로고
    • A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials
    • Epub ahead of print 3 September 2014. DOI: 10.1177/1077546314543727
    • Dehghan M, Hamedi EA, Khosravian-Arab H, (2014) A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials. Journal of Vibration and Control. Epub ahead of print 3 September 2014. DOI: 10.1177/1077546314543727.
    • (2014) Journal of Vibration and Control
    • Dehghan, M.1    Hamedi, E.A.2    Khosravian-Arab, H.3
  • 18
    • 70549084939 scopus 로고    scopus 로고
    • Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients
    • Ding Z, Xiao A, Li M, (2010) Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients. Journal of Computational and Applied Mathematics 233 (8): 1905-1914.
    • (2010) Journal of Computational and Applied Mathematics , vol.233 , Issue.8 , pp. 1905-1914
    • Ding, Z.1    Xiao, A.2    Li, M.3
  • 19
    • 84892836298 scopus 로고    scopus 로고
    • Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1 + 1 nonlinear Schrödinger equations
    • Doha E, Bhrawy A, Abdelkawy M, Van Gorder RA, (2014a) Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1 + 1 nonlinear Schrödinger equations. Journal of Computational Physics 261: 244-255.
    • (2014) Journal of Computational Physics , vol.261 , pp. 244-255
    • Doha, E.1    Bhrawy, A.2    Abdelkawy, M.3    Van Gorder, R.A.4
  • 20
    • 84888631283 scopus 로고    scopus 로고
    • A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations
    • Doha E, Bhrawy A, Baleanu D, Hafez R, (2014b) A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations. Applied Numerical Mathematics 77: 43-54.
    • (2014) Applied Numerical Mathematics , vol.77 , pp. 43-54
    • Doha, E.1    Bhrawy, A.2    Baleanu, D.3    Hafez, R.4
  • 21
    • 79960555480 scopus 로고    scopus 로고
    • Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
    • Doha E, Bhrawy A, Ezz-Eldien S, (2011) Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Applied Mathematical Modelling 35 (12): 5662-5672.
    • (2011) Applied Mathematical Modelling , vol.35 , Issue.12 , pp. 5662-5672
    • Doha, E.1    Bhrawy, A.2    Ezz-Eldien, S.3
  • 22
    • 84861893481 scopus 로고    scopus 로고
    • A new Jacobi operational matrix: An application for solving fractional differential equations
    • Doha E, Bhrawy A, Ezz-Eldien S, (2012) A new Jacobi operational matrix: An application for solving fractional differential equations. Applied Mathematical Modelling 36 (10): 4931-4943.
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.10 , pp. 4931-4943
    • Doha, E.1    Bhrawy, A.2    Ezz-Eldien, S.3
  • 23
    • 84884238940 scopus 로고    scopus 로고
    • Application of the collocation method for solving nonlinear fractional integro-differential equations
    • Eslahchi M, Dehghan M, Parvizi M, (2014) Application of the collocation method for solving nonlinear fractional integro-differential equations. Journal of Computational and Applied Mathematics 257: 105-128.
    • (2014) Journal of Computational and Applied Mathematics , vol.257 , pp. 105-128
    • Eslahchi, M.1    Dehghan, M.2    Parvizi, M.3
  • 24
    • 85006379921 scopus 로고    scopus 로고
    • A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
    • Epub ahead of print 3 March 2015. DOI: 10.1177/1077546315573916
    • Ezz-Eldien S, Doha E, Baleanu D, Bhrawy A, (2015) A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems. Journal of Vibration and Control. Epub ahead of print 3 March 2015. DOI: 10.1177/1077546315573916.
    • (2015) Journal of Vibration and Control
    • Ezz-Eldien, S.1    Doha, E.2    Baleanu, D.3    Bhrawy, A.4
  • 25
    • 78751643802 scopus 로고    scopus 로고
    • On the use of matrix functions for fractional partial differential equations
    • Garrappa R, Popolizio M, (2011) On the use of matrix functions for fractional partial differential equations. Mathematics and Computers in Simulation 81 (5): 1045-1056.
    • (2011) Mathematics and Computers in Simulation , vol.81 , Issue.5 , pp. 1045-1056
    • Garrappa, R.1    Popolizio, M.2
  • 27
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He JH, (1998) Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 167 (1): 57-68.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.167 , Issue.1 , pp. 57-68
    • He, J.H.1
  • 28
    • 0012866112 scopus 로고
    • Spectral methods with sparse matrices
    • Heinrichs W, (1989) Spectral methods with sparse matrices. Numerische Mathematik 56 (1): 25-41.
    • (1989) Numerische Mathematik , vol.56 , Issue.1 , pp. 25-41
    • Heinrichs, W.1
  • 29
    • 84896885047 scopus 로고    scopus 로고
    • Numerical solution for a class of fractional convection-diffusion equations using the flatlet oblique multiwavelets
    • Irandoust-Pakchin S, Dehghan M, Abdi-Mazraeh S, Lakestani M, (2014) Numerical solution for a class of fractional convection-diffusion equations using the flatlet oblique multiwavelets. Journal of Vibration and Control 20 (6): 913-924.
    • (2014) Journal of Vibration and Control , vol.20 , Issue.6 , pp. 913-924
    • Irandoust-Pakchin, S.1    Dehghan, M.2    Abdi-Mazraeh, S.3    Lakestani, M.4
  • 31
    • 84896826819 scopus 로고    scopus 로고
    • A method for obtaining the operational matrix of fractional Jacobi functions and applications
    • Kayedi-Bardeh A, Eslahchi M, Dehghan M, (2014) A method for obtaining the operational matrix of fractional Jacobi functions and applications. Journal of Vibration and Control 20 (5): 736-748.
    • (2014) Journal of Vibration and Control , vol.20 , Issue.5 , pp. 736-748
    • Kayedi-Bardeh, A.1    Eslahchi, M.2    Dehghan, M.3
  • 32
    • 84901191174 scopus 로고    scopus 로고
    • A new method based on Legendre polynomials for solutions of the fractional two-dimensional heat conduction equation
    • Khalil H, Khan RA, (2014) A new method based on Legendre polynomials for solutions of the fractional two-dimensional heat conduction equation. Computers & Mathematics with Applications 67 (10): 1938-1953.
    • (2014) Computers & Mathematics with Applications , vol.67 , Issue.10 , pp. 1938-1953
    • Khalil, H.1    Khan, R.A.2
  • 33
    • 0034598769 scopus 로고    scopus 로고
    • Fractal stream chemistry and its implications for contaminant transport in catchments
    • Kirchner JW, Feng X, Neal C, (2000) Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 403 (6769): 524-527.
    • (2000) Nature , vol.403 , Issue.6769 , pp. 524-527
    • Kirchner, J.W.1    Feng, X.2    Neal, C.3
  • 34
    • 84902875938 scopus 로고    scopus 로고
    • The Legendre condition of the fractional calculus of variations
    • Lazo MJ, Torres DF, (2014) The Legendre condition of the fractional calculus of variations. Optimization 63 (8): 1157-1165.
    • (2014) Optimization , vol.63 , Issue.8 , pp. 1157-1165
    • Lazo, M.J.1    Torres, D.F.2
  • 35
  • 38
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • Meerschaert MM, Tadjeran C, (2006) Finite difference approximations for two-sided space-fractional partial differential equations. Applied Numerical Mathematics 56 (1): 80-90.
    • (2006) Applied Numerical Mathematics , vol.56 , Issue.1 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 40
    • 84899622362 scopus 로고    scopus 로고
    • High-order difference scheme for the solution of linear time fractional Klein-Gordon equations
    • Mohebbi A, Abbaszadeh M, Dehghan M, (2014) High-order difference scheme for the solution of linear time fractional Klein-Gordon equations. Numerical Methods for Partial Differential Equations 30 (4): 1234-1253.
    • (2014) Numerical Methods for Partial Differential Equations , vol.30 , Issue.4 , pp. 1234-1253
    • Mohebbi, A.1    Abbaszadeh, M.2    Dehghan, M.3
  • 42
    • 84890888593 scopus 로고    scopus 로고
    • A discrete time method to the first variation of fractional order variational functionals
    • Pooseh S, Almeida R, Torres DF, (2013) A discrete time method to the first variation of fractional order variational functionals. Central European Journal of Physics 11 (10): 1262-1267.
    • (2013) Central European Journal of Physics , vol.11 , Issue.10 , pp. 1262-1267
    • Pooseh, S.1    Almeida, R.2    Torres, D.F.3
  • 43
    • 85027939449 scopus 로고    scopus 로고
    • Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems
    • Raja MAZ, Chaudhary NI, (2015) Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems. Signal Processing 107: 327-339.
    • (2015) Signal Processing , vol.107 , pp. 327-339
    • Raja, M.A.Z.1    Chaudhary, N.I.2
  • 44
    • 84877270201 scopus 로고    scopus 로고
    • Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis
    • Rostamy D, Alipour M, Jafari H, Baleanu D, (2013) Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis. Romanian Reports in Physics 65 (2): 334-349.
    • (2013) Romanian Reports in Physics , vol.65 , Issue.2 , pp. 334-349
    • Rostamy, D.1    Alipour, M.2    Jafari, H.3    Baleanu, D.4
  • 45
    • 84887591850 scopus 로고    scopus 로고
    • Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
    • Wang H, Du N, (2014) Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations. Journal of Computational Physics 258: 305-318.
    • (2014) Journal of Computational Physics , vol.258 , pp. 305-318
    • Wang, H.1    Du, N.2
  • 46
    • 84988289226 scopus 로고    scopus 로고
    • A parareal method for time-fractional differential equations
    • Xu Q, Hesthaven JS, Chen F, (2015) A parareal method for time-fractional differential equations. Journal of Computational Physics 293: 173-183.
    • (2015) Journal of Computational Physics , vol.293 , pp. 173-183
    • Xu, Q.1    Hesthaven, J.S.2    Chen, F.3


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