Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind

Journal of Mathematical Analysis and Applications

Volumn 324, Issue 1, 2006, Pages 225-237

  Tao, Lü ^a   Yong, Huang ^b  

^a SICHUAN UNIVERSITY   (China)

^b Sichuan University   (China)

Author keywords

A posteriori estimate; Nonlinear weakly singular Volterra equation; The asymptotic expansion

Indexed keywords

EID: 33748904596     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.12.013     Document Type: Article

References (16)

1. Baker C.T.H., and Miller G.F. The Numerical Treatment of Integral Equation (1977), Clarendon, Oxford
2. In: Baker C.T.H., and Miller G.F. (Eds). Treatment of Integral Equation by Numeric Methods (1982), Academic Press, London
3. Baratella P., and Palamara Orsi A. A new approach to the numerical solution of weakly singular Volterra integral equations. J. Comput. Appl. Math. 163 (2004) 401-418
4. Brunner H. The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes. Math. Comp. 45 (1985) 417-437
5. Brunner H., and Evans M.D. Piecewise polynomial collocation for Volterra type integral equations of the second kind. J. Inst. Math. Appl. 20 (1977) 415-423
6. Brunner H. The numerical solution of integral equations with weakly singular kernels. In: Griffths D.F. (Ed). Numerical Analysis (1984), Springer, Berlin 50-71
7. Delves L.M., and Mohamed J.L. Computational Methods for Integral Equations (1985), Cambridge Univ. Press, Cambridge
8. Davis P.L., and Rabinowitz P. Methods of Numeric Integration. second ed. (1984), Academic Press, New York
9. Hu Q. Superconvergence of numerical solutions to Volterra integral equations with singularities. SIAM J. Numer. Anal. 34 (1997) 1698-1707
10. Kershaw D. Some results for Volterra integral equations of the second kind. In: Baker C.T.H., and Miller G.F. (Eds). Treatment of Integral Equation by Numeric Methods (1982), Academic Press, London 273-282
11. Liem C.B., Tao L., and Shih T.M. The Splitting Extrapolation Method (1995), World Scientific, Singapore
12. Tao L., and Yong H. A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind. J. Math. Anal. Appl. 282 (2003) 56-62
13. Lubich C. Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Math. Comp. 45 (1985) 463-469
14. Marchuk G.I., and Shaidurov V.V. Difference Methods and Their Extrapolations (1983), Springer, New York
15. Navot I. A further extension of Euler-Maclaurin summation formula. J. Math. Phys. 41 (1962) 155-184
16. Palamara Orsi A. Product integration for Volterra integral equations of the second kind with weakly singular kernels. Math. Comp. 65 (1996) 1201-1212