References
- Asadzadeh , M. , Schatz , A. and Wendland , W. 2009 . A new approach to Richardson extrapolation in the finite element method for second order elliptic problems . Math. Comp. , 78 : 1951 – 1973 .
- Baratella , P. and Orsi , A. P. 2004 . A new approach to the numerical solution of weakly singular Volterra integral equations . J. Comput. Appl. Math. , 163 : 401 – 418 .
- Basombrío , F. G. , Guarracino , L. and Vénere , M. J. 2006 . A non-iterative algorithm based on Richardson's extrapolation. Application to groundwater flow modelling . Internat. J. Numer. Methods Eng. , 65 : 1088 – 1112 .
- Berenguer , M. I. , Gámez , D. , Garralda-Guillem , A. I. , Ruiz Galán , M. and Serrano Pérez , M. C. 2011 . Biorthogonal systems for solving Volterra integral equation systems of the second kind . J. Comput. Appl. Math. , 235 : 1875 – 1883 .
- Bickel , P. J. and Yahav , J. A. 1988 . Richardson extrapolation and the bootstrap . J. Amer. Statist. Assoc. , 83 : 387 – 393 .
- Blum , H. , Lin , Q. and Rannacher , R. 1986 . Asymptotic error expansion and Richardson extrapolation for linear finite elements . Numer. Math. , 49 : 11 – 37 .
- Brezinski , C. and Redivo-Zaglia , M. 1991 . Extrapolation Methods: Theory and Practice , Amsterdam : North-Holland .
- Brezinski , C. and Redivo-Zaglia , M. 2010 . Extended procedures for extrapolation to the limit . J. Comput. Appl. Math. , 235 : 631 – 645 .
- Burg , C. and Erwin , T. 2009 . Application of Richardson extrapolation to the numerical solution of partial differential equations . Numer. Methods Partial Differential Equations , 25 : 810 – 832 .
- Cao , Y. , He , X.-M. and Lü , T. 2009 . A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements . J. Comput. Phys. , 228 : 109 – 122 .
- Cao , Y. , He , X.-M. and Lü , T. 2011 . An algorithm using finite volume element method and its splitting extrapolation . J. Comput. Appl. Math. , 235 : 3734 – 3742 .
- Chen , C. M. and Shih , T. 1998 . Finite Element Methods for Integrodifferential Equations , Singapore : World Scientific Publishing .
- Chen , C. M. , Liu , F. and Anh , V. 2009 . A Fourier method and an extrapolation technique for Stokes’ first problem for a heated generalized second grade fluid with fractional derivative . J. Comput. Appl. Math. , 223 : 777 – 789 .
- Chen , Z. , Long , G. and Nelakanti , G. 2009 . Richardson extrapolation of iterated discrete projection methods for eigenvalue approximation . J. Comput. Appl. Math. , 223 : 48 – 61 .
- De Bonis , M. C. and Mastroianni , G. 2009 . Nyström method for systems of integral equations on the real semiaxis . IMA J. Numer. Anal. , 29 : 632 – 650 .
- Delves , L. M. and Mohamed , J. L. 1985 . Computational Methods for Integral Equations , London : Cambridge University Press .
- Dutka , J. 1984 . Richardson extrapolation and Romberg integration . Historia Math. , 11 : 3 – 21 .
- Fairweather , G. , Lin , Q. , Lin , Y. , Wang , J. and Zhang , S. 2006 . Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods . SIAM J. Numer. Anal. , 44 : 1122 – 1149 .
- Fössmeier , R. 1989 . On Richardson extrapolation for finite difference methods on regular grids . Numer. Math. , 55 : 451 – 462 .
- Grinberg , L. and Karniadakis , G. 2011 . Extrapolation-based acceleration of iterative solvers: Application to simulation of 3D flows . Commun. Comput. Phys. , 9 : 607 – 626 .
- Han , G. and Wang , R. 2002 . Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations . J. Comput. Appl. Math. , 139 : 49 – 63 .
- Hashemiparast , S. M. , Fallahgoul , H. and Hosseyni , A. 2010 . Fourier series approximation for periodic solution of system of integral equations using Szego–Bernstein weights . Int. J. Comput. Math. , 87 : 485 – 1496 .
- He , X.-M. and Lü , T. 2007 . Splitting extrapolation method for solving second order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements . Int. J. Comput. Math. , 84 : 767 – 781 .
- He , X.-M. and Lü , T. 2009 . A finite element splitting extrapolation for second order hyperbolic equations . SIAM J. Sci. Comput. , 31 : 4244 – 4265 .
- Heiden , U. 1980 . Analysis of Neural Networks , New York : Springer-Verlag .
- Huang , J. and Wang , Z. 2009/10 . Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods . SIAM J. Sci. Comput. , 31 : 4115 – 4129 .
- Huang , Y. , Fang , M. and Li , X.-F. 2009 . Approximate solution of a system of linear integral equations by the Taylor expansion method . Int. J. Comput. Math. , 86 : 924 – 937 .
- Jia , S. , Xie , H. , Yin , X. and Gao , S. 2008 . Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods . Numer. Methods Partial Differential Equations , 24 : 435 – 448 .
- Jung , M. and Rüde , U. 1996 . Implicit extrapolation methods for multilevel finite element computations . SIAM J. Sci. Comput. , 17 : 156 – 179 .
- Jung , M. and Rüde , U. 1998 . Implicit extrapolation methods for variable coefficient problems . SIAM J. Sci. Comput. , 19 : 1109 – 1124 .
- Johansson , B. and Christer , V. 1993 . The use of Richardson extrapolation for the numerical solution of low Mach number flow in confined regions . J. Sci. Comput. , 8 : 307 – 340 .
- Kress , R. 1989 . Linear Integral Equations , Berlin : Springer-Verlag .
- Li , M. , Lin , Q. and Zhang , S. 2010 . Extrapolation and superconvergence of the Steklov eigenvalue problem . Adv. Comput. Math. , 33 : 25 – 44 .
- Liem , C. B. , Lü , T. and Shih , T. M. 1995 . The Splitting Extrapolation Method , World Scientific, Singapore .
- Lin , T. , Lin , Y. , Rao , M. and Zhang , S. 2000 . Petrov–Galerkin methods for linear Volterra integro-differential equations . SIAM J. Numer. Anal. , 38 : 937 – 963 .
- Liu , Y. and Lü , T. 2007 . Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations . J. Comput. Appl. Math. , 201 : 300 – 313 .
- Lü , T. and Huang , Y. 2003 . A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equation of the second kind . J. Math. Anal. Appl. , 282 : 56 – 62 .
- Lu , T. and Huang , Y. 2006 . Extrapolation method for solving weakly singular Volterra integral equations of the second kind . J. Math. Anal. Appl. , 324 : 225 – 237 .
- Maleknejad , K. and Shahrezaee , M. 2004 . Using Runge–Kutta method for numerical solution of the system of Volterra integral equation . Appl. Math. Comput. , 149 : 399 – 410 .
- Maleknejad , K. and Shamloo , A. S. 2008 . Numerical solution of singular Volterra integral equations system of convolution type by using operational matrices . Appl. Math. Comput. , 195 : 500 – 505 .
- Marchuk , G. and Shaĭdurov , V. 1983 . Difference Methods and Their Extrapolations. Translated from the Russian , New York : Springer-Verlag . Applications of Mathematics Vol. 19
- Marcozzi , M. D. 2009 . Extrapolation discontinuous Galerkin method for ultraparabolic equations . J. Comput. Appl. Math. , 224 : 679 – 687 .
- Mitrinovic , D. S. and Vasic , P. M. 1970 . Analysis Inequalities , Berlin : Springer .
- Moiseiwitsch , B. L. 2005 . Integral Equations , New York : Dover Publications Inc .
- Navot , J. 1962 . A further extension of Euler–Maclaurin summation formula . J. Math. Phys. , 41 : 155 – 184 .
- Pandey , R. K. , Singh , O. P. and Singh , V. K. 2009 . Numerical solution of system of Volterra integral equations using Bernstein plynomials . Int. J. Nonlinear Sci. Numer. , 10 : 891 – 895 .
- Rahul , K. and Bhattacharyya , S. N. 2006 . One-sided finite-difference approximations suitable for use with Richardson extrapolation . J. Comput. Phys. , 219 : 13 – 20 .
- Saeed , R. K. and Ahmed , C. S. 2008 . Numerical solution of the system of linear Volterra integral equations of the second kind using Mote-Carlo method . J. Appl. Sci. Res , 4 ( 10 ) : 1174 – 1181 .
- Sidi , A. 2000 . The Richardson extrapolation process with a harmonic sequence of collocation points . SIAM J. Numer. Anal. , 37 : 1729 – 1746 .
- Sidi , A. 2010 . Asymptotic analysis of a generalized Richardson extrapolation process on linear sequences . Math. Comp. , 79 : 1681 – 1695 .
- Tahmasbi , A. and Fard , O. S. 2008 . Numerical solution of linear Volterra integral equations system of the second kind . Appl. Math. Comput. , 201 : 547 – 552 .
- Wang , Y. 2011 . Error and extrapolation of a compact LOD method for parabolic differential equations . J. Comput. Appl. Math. , 235 : 1367 – 1382 .
- Wang , Y. and Zhang , J. 2009 . Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation . J. Comput. Phys. , 228 : 137 – 146 .
- Wu , G. and Wei , Y. 2010 . An Arnoldi-extrapolation algorithm for computing PageRank . J. Comput. Appl. Math. , 234 : 3196 – 3212 .
- Zarebnia , M. and Rashidinia , J. 2010 . Approximate solution of systems of Volterra integral equations with error analysis . Int. J. Comput. Math. , 87 : 3052 – 3062 .
- Zlatev , Z. , Faragó , I. and Havasi , Á. 2010 . Stability of the Richardson extrapolation applied together with the θ-method . J. Comput. Appl. Math. , 235 : 507 – 517 .