Meshless simulations of the two-dimensional fractional-time convection–diffusion–reaction equations

Engineering Analysis with Boundary Elements - Tập 36 - Trang 1522-1527 - 2012
Ahmad Shirzadi1, Leevan Ling2, Saeid Abbasbandy3
1Department of Mathematics, Persian Gulf University, Bushehr, Iran
2Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
3Department of Mathematics, Imam Khomeini International University, Ghazvin, 34149, Iran

Tài liệu tham khảo

Adams, 1992, Field study of dispersion in a heterogeneous aquifer. 2. Spatial moments analysis, Water Resour Res, 28, 3293, 10.1029/92WR01757 Sun, 2010, Fractional differential models for anomalous diffusion, Physica A, 389, 2719, 10.1016/j.physa.2010.02.030 Chen, 2010, Anomalous diffusion modeling by fractal and fractional derivatives, Comput Math Appl, 59, 1754, 10.1016/j.camwa.2009.08.020 Gorenflo, 2002, Time fractional diffusion: a discrete random walk approach, Nonlinear Dyn, 29, 129, 10.1023/A:1016547232119 Gorenflo, 2007, Continuous-time random walk and parametric subordination in fractional diffusion, Chaos Solitons Fractals, 34, 87, 10.1016/j.chaos.2007.01.052 Metzler, 2000, Boundary value problems for fractional diffusion equations, Physica A, 278, 107, 10.1016/S0378-4371(99)00503-8 Metzler, 2000, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys Rep, 339, 77, 10.1016/S0370-1573(00)00070-3 Babouskos, 2010, Nonlinear vibrations of viscoelastic plates of fractional derivative type: an AEM solution, Open Mech J, 4, 8, 10.2174/1874158401004010008 Katsikadelis, 2009, Numerical solution of multi-term fractional differential equations, ZAMM—J Appl Math Mech [Z Angew Math Mech], 89, 593, 10.1002/zamm.200900252 Katsikadelis, 2010, Post-buckling analysis of viscoelastic plates with fractional derivative models, Eng Anal Boundary Elem, 34, 1038, 10.1016/j.enganabound.2010.07.003 Nerantzaki, 2011, Analysis of inhomogeneous anisotropic viscoelastic bodies described by multi-parameter fractional differential constitutive models, Comput Math Appl, 62, 945, 10.1016/j.camwa.2011.05.003 Katsikadelis, 2011, The BEM for numerical solution of partial fractional differential equations, Comput Math Appl, 62, 891, 10.1016/j.camwa.2011.04.001 Brunner, 2010, Numerical simulations of 2D fractional subdiffusion problems, J Comput Phys, 229, 6613, 10.1016/j.jcp.2010.05.015 Ling, 2006, Results on meshless collocation techniques, Eng Anal Boundary Elem, 30, 247, 10.1016/j.enganabound.2005.08.008 Ling, 2008, Stable and convergent unsymmetric meshless collocation methods, SIAM J Numer Anal, 46, 1097, 10.1137/06067300X Kansa, 1990, Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates, Comput Math Appl, 19, 127, 10.1016/0898-1221(90)90270-T Belytschko, 1994, Element-free Galerkin methods, Int J Numer Methods Eng, 37, 229, 10.1002/nme.1620370205 Libre, 2008, A fast adaptive wavelet scheme in RBF collocation for nearly singular potential PDEs, CMES—Comput Modeling Eng Sci, 38, 263 Libre, 2009, A multiresolution prewavelet-based adaptive refinement scheme for RBF approximations of nearly singular problems, Eng Anal Boundary Elem, 33, 901, 10.1016/j.enganabound.2009.02.007 Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput Mech, 22, 117, 10.1007/s004660050346 Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation, Comput Modeling Simulation Eng, 3, 187 Atluri, 2004 Atluri, 2002 Abbasbandy, 2010, A meshless method for two-dimensional diffusion equation with an integral condition, Eng Anal Boundary Elem, 34, 1031, 10.1016/j.enganabound.2010.07.002 Abbasbandy, 2011, MLPG method for two-dimensional diffusion equation with Neumann's and non-classical boundary conditions, Appl Numer Math, 61, 170, 10.1016/j.apnum.2010.09.002 Mirzaei, 2010, MLPG approximation to the p-Laplace problem, Comput Mech, 46, 805, 10.1007/s00466-010-0521-1 Dehghan, 2009, Meshless local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity, Appl Numer Math, 59, 1043, 10.1016/j.apnum.2008.05.001 Sladek, 2010, Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG, Int J Solids Struct, 47, 1381, 10.1016/j.ijsolstr.2010.01.025 Sladek, 2005, Stress analysis in anisotropic functionally graded materials by the MLPG method, Eng Anal Boundary Elem, 29, 597, 10.1016/j.enganabound.2005.01.011 Sladek, 2008, Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG, Comput Mech, 42, 697, 10.1007/s00466-008-0269-z Sladek, 2006, Inverse heat conduction problems by meshless local Petrov–Galerkin method, Eng Anal Boundary Elem, 30, 650, 10.1016/j.enganabound.2006.03.003 Dehghan, 2010, Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM), Comput Phys Commun, 181, 772, 10.1016/j.cpc.2009.12.010 Mirzaei, 2010, Meshless local Petrov–Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation, J Comput Appl Math, 233, 2737, 10.1016/j.cam.2009.11.022 Mirzaei, 2010, A meshless based method for solution of integral equations, Appl Numer Math, 60, 245, 10.1016/j.apnum.2009.12.003 Brunner, 2007, High-order collocation methods for singular Volterra functional equations of neutral type, Appl Numer Math, 57, 533, 10.1016/j.apnum.2006.07.006 Brunner, 2001, Piecewise polynomial collocation methods for linear Volterra integrodifferential equations with weakly singular kernels, SIAM J Numer Anal, 39, 957, 10.1137/S0036142900376560 Abbasbandy, 2011, Numerical simulations for coupled pair of diffusion equations by MLPG method, CMES—Comput Modeling Eng Sci, 71, 15