%0 Journal Article %T The Analytical Solution of Singularly Perturbed Boundary Value Problems %A Hosseini, S. Gh. %A Hosseini, S. M. %A Heydari, M. %A Amini, M. %J Journal of Mathematics and Computer Science %D 2014 %V 10 %N 1 %@ ISSN 2008-949X %F Hosseini2014 %X In this paper, we present an algorithm for approximating numerical solution of singularly perturbed boundary value problems by means of homotopy analysis and tau Bernestein polynomial method. The method is tested for several problems and the results demonstrate reliability and efficiency of the method. %9 journal article %R 10.22436/jmcs.010.01.02 %U http://dx.doi.org/10.22436/jmcs.010.01.02 %P 7-22 %0 Journal Article %T Fitted fourth-order tridiagonal finite difference method for singular perturbation problems %A A. Andargie %A Y. N. Reddy %J Appl. Math. Comp. %D 2007 %V 192 %F Andargie2007 %0 Journal Article %T Numerical treatment of singularly perturbed two point boundary value problems exhibiting boundary layers %A B. S. Attili %J Commun. Nonlinear Sci. Numer. Simulat %D In Press %V %F Attili In Press %0 Book %T Advanced Mathematical Methods for Scientists and Engineers %A C. M. Bender %A S. A. Orszag %D 1978 %I McGraw-Hill %C New York %F Bender1978 %0 Journal Article %T A variational difference scheme for a boundary value problem with a small parameter multiplying the highest derivative %A I. P. Boglaev %J Zh. Vychisl. Mat. i Mat. Fiz. %D 1981 %V 21 %F Boglaev1981 %0 Journal Article %T A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems %A Zh. Cen %A A. Xu %A A. Le %J J. Comp. Appl. Math. %D 2010 %V 234 %F Cen2010 %0 Journal Article %T Asymptotic solutions of singularly perturbed second-order differential equations and application to multi-point boundary value problems %A Z. Dua %A L. Kong %J Appl. Math. Letters %D 2010 %V 23 %F Dua2010 %0 Journal Article %T Homotopy perturbation technique %A J. H. He %J Comput. Methods Appl. Mech. Eng. %D 1999 %V 178 %F He1999 %0 Journal Article %T Approximate analytical solution of Blasius equation %A J. H. He %J Commum. Nonlinear Sci. Numer. Simul. %D 1998 %V 3 %F He1998 %0 Journal Article %T A coupling method of homotopy technique and perturbation technique for nonlinear problems %A J. H. He %J Internat. J. NonLinear Mech. %D 2000 %V 35 (1) %F He2000 %0 Journal Article %T A simple perturbation approach to Blasius equation %A J. H. He %J Appl. Math. Comput. %D 2003 %V 140 %F He2003 %0 Journal Article %T A new algorithm for general singularly perturbed two-point boundray value problems %A H. M. Habib %A E. R. El-zahar %J Advances in Differential Equations and Control Processes %D 2008 %V 1 %F Habib2008 %0 Journal Article %T Initial-value technique for a class of nonlinear singular perturbation problems %A M. K. Kadalbajoo %A Y. N. Reddy %J J. Optim. Theo. Appl. %D 1987 %V 53 %F Kadalbajoo1987 %0 Book %T Perturbation Methods in Applied Mathematics %A J. Kevorkian %A J. D. Cole %D 1981 %I Springer-Verlag %C New York %F Kevorkian1981 %0 Journal Article %T On the convergence uniformly in e of difference schemes for a two point boundary singular perturbation problem %A J. J. H. Miller %J In Numerical analysis of singular perturbation problems (Proc. Conf. Math. Inst. Catholic Univ. Nijmegen 1978) Academic Press, London %D 1979 %V %F Miller1979 %0 Journal Article %T Parameter-uniform numerical method for global solution and global normalized flux of singularly perturbed boundary value problems using grid equidistribution %A J. Mohapatraa %A S. Natesan %J Comput. Math. Appl. %D 2010 %V 60 %F Mohapatraa2010 %0 Journal Article %T Numerical Solution of Singularly Perturbed Boundary Value Problems Based on Optimal Control Strategy %A G. B. Loghmani %A M. Ahmadinia %J Acta Appl. Math. %D 2010 %V 112 %F Loghmani2010 %0 Journal Article %T Optimal B-spline collocation method for self-adjoint singularly perturbed boundary value problems %A S. C. S. Rao %A M. Kumar %J Appl. Math. Comput. %D 2007 %V 188 %F Rao2007 %0 Journal Article %T An asymptotic finite element method for singularly perturbed third and fourth order ordinary differential equations with discontinuous source term %A A. Ramesh %A N. Ramanujam %J Appl. Math. Comp. %D 2007 %V 191 %F Ramesh2007 %0 Journal Article %T Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives %A J. Rashidinia %A R. Mohammadi %A M. Ghasemi %J Appl. Math. Comp. %D 2007 %V 190 %F Rashidinia2007 %0 Journal Article %T Numerical integration method for general singularly perturbed two point boundary value problems %A Y. N. Reddy %A P. P. Chakravarthy %J Appl. Math. Comput. %D 2002 %V 133 %F Reddy2002 %0 Journal Article %T An initial-value approach for solving singular perturbed two-point boundary value problems %A Y. N. Reddy %A P. P. Chakravarthy %J Appl. Math. Comput. %D 2004 %V 155 %F Reddy2004 %0 Journal Article %T An exponentially fitted finite difference method for singular perturbation problems %A Y. N. Reddy %A P. P. Chakravarthy %J Appl. Math. Comput. %D 2004 %V 154 %F Reddy2004 %0 Journal Article %T Singular perturbations of difference methods for linear ordinary differential equations %A H. J. Reinhardt %J Appl. Anal. %D 1980 %V 10 %F Reinhardt1980 %0 Journal Article %T On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions %A A. H. Schatz %A L. B. Wahlbin %J Math. Comput. %D 1983 %V 40 %F Schatz1983 %0 Journal Article %T Spline collocation method for singular perturbation problem %A M. Stojanovic %J Glas. Mat. Ser. III %D 2002 %V 37 %F Stojanovic2002 %0 Journal Article %T Some possibilities of applying spline collocations to singular perturbation problems %A K. Surla %A V. Jerkovic %J In Numerical methods and approximation theory, II Univ. Novi Sad %D 1985 %V 10 %F Surla1985 %0 Journal Article %T Numerical solution of KdV equation using modified Bernstein polynomials %A D. D. Bhatta %A M. I. Bhatti %J Appl. Math. Comput. %D 2006 %V 174 %F Bhatta2006 %0 Journal Article %T Numerical solution of some classes of integral equations using Bernstein polynomials %A B. N. Mandal %A S. Bhattacharya %J Appl. Math. Comput. %D 2007 %V 190 %F Mandal2007 %0 Journal Article %T Solutions of differential equations in a Bernstein polynomial basis %A M. I. Bhatti %A P. Bracken %J J. Comput. Appl. Math. %D 2007 %V 205 %F Bhatti2007 %0 Journal Article %T Use of Bernstein polynomials in numerical solutions of Volterra integral equations %A S. Bhattacharya %A B. N. Mandal %J Appl. Math. Sci. %D 2008 %V 2 %F Bhattacharya2008 %0 Journal Article %T Approximate solutions of Fredholm integral equations of the second kind %A A. Chakrabarti %A S. C. Martha %J Appl. Math. Comput. %D 2009 %V 211 %F Chakrabarti2009 %0 Journal Article %T The Bernstein operational matrix of integration %A A. K. Singh %A V. K. Singh %A O. P. Singh %J Appl. Math. Sci. %D 2009 %V 3 %F Singh2009 %0 Journal Article %T Operational matrices of Bernstein polynomials and their applications %A S. A. Yousefi %A M. Behroozifar %J Int. J. Syst. Sci. %D 2010 %V 41 %F Yousefi2010 %0 Journal Article %T The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass %A S. A. Yousefi %A M. Behroozifar %A M. Dehghan %J J. Comput. Appl. Math. %D 2011 %V 235 %F Yousefi2011 %0 Journal Article %T On the derivatives of Bernstein polynomials: An application for the solution of high even-order differential equations %A E. H. Doha %A A. H. Bhrawy %A M. A. Saker %J Bound. Value. Probl. %D doi:10.1155/2011/829543. %V %F Dohadoi:10.1155/2011/829543. %0 Journal Article %T Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations %A E. H. Doha %A A. H. Bhrawy %A M. A. Saker %J Appl. Math. Lett. %D 2011 %V 24 %F Doha2011 %0 Journal Article %T Numerical solution of the nonlinear age-structured population models by using the operational matrices of Bernstein polynomials %A S. A. Yousefi %A M. Behroozifar %A M. Dehghan %J Appl. Math. Model. %D 2012 %V 36 %F Yousefi2012 %0 Journal Article %T Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations %A K. Maleknejad %A E. Hashemizadeh %A B. Basirat %J Commun. Nonlinear. Sci. Numer. Simulat. %D 2012 %V 17 %F Maleknejad2012 %0 Journal Article %T Bernstein polynomials for solving fractional heat- and wave-like equations %A D. Rostamy %A K. Karimi %J Fract. Calc. Appl. Anal. %D 2012 %V 15 %F Rostamy2012 %0 Book %T %A S. J. Liao %A Ph. D. Thesis %D 1992 %I Shanghai Jiao Tong University, Shanghai %C Chaina %F Liao1992 %0 Book %T Beyond perturbation: introduction to the homotopy analysis method %A S. J. Liao %D 2003 %I CRC Press %C Boca Raton: Chapman Hall %F Liao2003 %0 Journal Article %T Homotopy analysis method for heat radiation equations %A S. Abbasbandy %J International Communications in Heat and Mass Transfer %D 2007 %V 34 %F Abbasbandy2007 %0 Journal Article %T Series solutions of nano boundary layer flows by means of the homotopy analysis method %A J. Cheng %A S. J. Liao %A R. N. Mohapatra %A K. Vajravelu %J J. Math. Anal. Appl. %D 2008 %V 343 %F Cheng2008 %0 Journal Article %T Homotopy analysis method for generalized Benjamin-Bona-Mahony equation %A S. Abbasbandy %J Z. angew. Math. Phys. %D 2008 %V 59 %F Abbasbandy2008 %0 Journal Article %T On a new reliable modification of homotopy analysis method %A A. Sami Bataineh %A M. S. M. Noorani %A I. Hashim %J Commun. Nonlinear Sci. Numer. Simulat. %D 2009 %V 14 %F Bataineh2009 %0 Journal Article %T Numerical solution of the generalized Zakharov equation by homotopy analysis method %A S. Abbasbandy %A E. Babolian %A M. Ashtiani %J Commun. Nonlinear Sci. Numer. Simulat. %D 2009 %V 14 %F Abbasbandy2009 %0 Journal Article %T Solution of the MHD Falkner-Skan flow by homotopy analysis method %A S. Abbasbandy %A T. Hayat %J Commun. Nonlinear Sci. Numer. Simulat. %D 2009 %V 14 %F Abbasbandy2009 %0 Journal Article %T Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method %A M. M. Rashidi %A S. Dinarvand %J Nonlinear Analysis: Real World Applications %D 2009 %V 10 %F Rashidi2009 %0 Journal Article %T Homotopy analysis method for the Kawahara equation %A S. Abbasbandy %J Nonlinear Analysis: Real World Applications %D 2010 %V 11 %F Abbasbandy2010 %0 Journal Article %T On explicit, purely analytic solutions of off-centered stagnation flow towards a rotating disc by means of HAM %A S. Dinarvand %J Nonlinear Analysis: Real World Applications %D 2010 %V 11 %F Dinarvand2010 %0 Journal Article %T Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method %A S. Abbasbandy %A E. Shivanian %J Commun. Nonlinear Sci. Numer. Simulat. %D 2010 %V 15 %F Abbasbandy2010 %0 Journal Article %T Solution of the Davey Stewartson equation using homotopy analysis method %A H. Jafari %A M. Alipour %J Nonlinear Analysis: Modelling and Control %D 2010 %V 15 %F Jafari2010 %0 Journal Article %T Numerical solution for Maxwells equation in metamaterials by Homotopy Analysis Method %A A. Zare %A M. A. Firoozjaee %J Journal of Mathematics and Computer Science %D 2011 %V 3 %F Zare2011 %0 Journal Article %T An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method %A H. M. Sedighi %A K. H. Shirazi %A J. Zare %J International Journal of Non-Linear Mechanics %D 2012 %V 47 %F Sedighi2012 %0 Journal Article %T Series solutions of non-Newtonian nanofluids with Reynolds model and Vogels model by means of the homotopy analysis method %A R. Ellahi %A M. Raza %A K. Vafai %J Mathematical and Computer Modelling %D 2012 %V 55 %F Ellahi2012 %0 Journal Article %T The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear agestructured population models %A M. Ghoreishi %A A. I. B. Md. Ismail %A A. K. Alomari %A A. S. Bataineh %J Commun. Nonlinear Sci. Numer. Simulat. %D 2012 %V 17 %F Ghoreishi2012 %0 Journal Article %T Solving a model for the evolution of smoking habit in Spain with homotopy analysis method %A F. Guerrero %A F. J. Santonja %A R. J. Villanueva %J Nonlinear Analysis: Real World Applications %D 2013 %V 14 %F Guerrero2013 %0 Journal Article %T The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions %A R. Ellahi %J Applied Mathematical Modelling %D 2013 %V 37 %F Ellahi2013 %0 Journal Article %T Analytical solutions Zakharov-Kuznetsov equations %A Touqeer Nawaz %A Ahmet Yildirim %A Syed Tauseef Mohyud-Din %J Advanced Powder Technology %D 2013 %V 24 %F Nawaz2013 %0 Journal Article %T A modification of the homotopy analysis method based on Chebyshev operational matrices %A M. Shaban %A S. Kazem %A J. A. Rad %J Mathematical and Computer Modelling %D In Press %V %F ShabanIn Press %0 Journal Article %T Some Notes on the Convergence Control Parameter in the Framework of the Homotopy Analysis Method %A J. Saeidian %A Sh. Javadi %J Journal of Mathematics and Computer Science %D 2014 %V 9 %F Saeidian2014 %0 Journal Article %T Unsteady linear viscoelastic fluid model over a stretching/shrinking sheet in the region of stagnation point flows %A Y. Khan %A A. Hussain %A N. Faraz %J Scientia Iranica %D In Press %V %F KhanIn Press %0 Book %T Spectral methods in fluid dynamics %A C. Canuto %A M. Y. Hussaini %A A. Quarteroni %A T. A. Zang %D 1988 %I Springer-Verlag %C New York %F Canuto 1988