NUMERICAL SOLUTION OF SINGULAR VOLTERRAINTEGRAL EQUATION VIA MIDPOINT METHOD
Abstract
This paper presents numerical scheme for solving singular Volterra integral equations via midpoint rule. The functions were approximated under the integrals by considering the non-variable subinterval. The convergence analysis of the error bound of the scheme is established. The numerical results show that the scheme has less number of iterations to obtain the best errors compared with other method
References
P. Lima and T. Diogo (2002) Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methods, Journal of Computational and Applied Mathematics 140 537-557.
P. Lima, T. Diogo (1997) An extrapolation method for a Volterra integral equation withweakly singular kernel, Applied Numerical Mathematics vol. 24, 131-148.
A.M. Wazwaz (2011) Linear and Nonlinear Integral Equations Methods and Applications, Springer Heidelberg Dordrecht London New York, Library of congress control no. 201192916.
T. Diogo, J.T Edwards, N.J Ford and S.M Thomas (2005) Numerical analysis of a singular integral equation, Applied Mathematics and Computation, 167, 372-382.
Teresa Diogo, Neville J. Ford, Pedro Lima and SvilenValtcheva (2005) Numerical methods for a Volterra integral equation with non-smooth solutions, Journal of Computational and Applied Mathematics, 189, 412423.
M. Rahman (2007) Integral Equations and their Applications, Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK, Library of Congress Catalog Card Number: 2007922339.
M.T. Diogo, P.M. Lima and M.S. Rebelo (2004) Comparative study of numerical methodsfor a nonlinear weakly singular Volterra integral equation, Journal of mathematics and mathematical sciences, vol.8.
T. Diogo, N.J. Ford, P.M. Lima and S.M. Thomas (2006) Solution of a Singular Integral Equation by a Split-Interval Method, International Journal of Numerical Analysis and Modelling. Number 1,Vol. 4 Pages 63-73.
T. Diogo, P. Lima (2007) Collocation Solutions of a Weakly Singular Volterra Integral Equation, TEMA Tend. Mat. Apl. Comput, 8, No. 2, 229-238.
T. Diogo, P. Lima (2008) Superconvergence of collocation methods for a class of weakly singular Volterra integral equations Journal of Computational and Applied Mathematics, Vol. 218, pp.307316.
C. Yang and J. Hou (2013) Numerical method for solving Volterra integral equations with a convolution kernel, Vol. IJAM, 43403..
T. Diogo (2009) Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations, Journal of Computational and Applied Mathematics Vol.229, pp.363372.
R.N. Prajapati, R. Mohan and P. Kumar (2012) Numerical Solution of Generalized Abels Integral Equation by Variational Iteration Method, American Journal of Computational Mathematics, Vol. 2, 312-315
S. Rahbar and E. Hashemizadeh (2008) A computational approach to the Fredholm Integral Equations of the second kind, Vol.2 pp 978-988.
Fawzi Abdelwahid (2010) Adomian Decomposition Method Applied to Nonlinear IntegralEquations, Alexandria Journal of Mathematics Vol. 1, No. 1, 2090-4320.
M.A Al-Jawary and A.MShehan (2015) Exact solutions for weakly singular Volterra integral equations by using an e_cient iterative method, IOSR Jour nal of Mathematics(IOSR-JM), vol.11, pp, 67-76.
A. Wazwaz, R. Rach and J.S. Duan (2013) The modified Adomian decomposition methodand the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm integral equations, Central European Journal of Engineering Vol.4 pp 669-678.
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