# NUMERICAL ALGORITHMS OF OPTIMAL COMPLEXITY FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS

## Related Articles

- Numerical solution of linear Fredholm and Volterra integral equation of second kind by using Gegenbauer wavelet. Singh, Rajeev Kumar; Mandal, B. N. // Journal of Advanced Research in Scientific Computing;2013, Vol. 5 Issue 3, p43
In this paper we present an efficient numerical method for solving Fredholm and Volterra integral equations of second kind by using Gegenbouer wavelet method . In the proposed method the unknown function in Fredholm and Volterra integral equation are approximated by using basis of Gegenbouer...

- Solving a System of Volterra-Fredholm Integral Equations of the Second kind via Fixed Point Method. Hasan, Talaat I.; Salleh, Shaharuddin; Sulaiman, Nejmaddin A. // AIP Conference Proceedings;2015, Vol. 1691, p1
In this paper, we consider the system of Volterra-Fredholm integral equations of the second kind (SVFI-2). We propose fixed point method (FPM) to solve SVFI-2. In addition, a few theorems and new algorithm is introduced. They are supported by numerical examples and simulations using Matlab. The...

- New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations. Dolapçı, İhsan Timuçin; Şeno, Mehmet; Pakdemirli, Mehmet // Journal of Applied Mathematics;2013, p1
In this paper, recently developed perturbation iterationmethod is used to solve FredholmandVolterra integral equations. Thestudy shows that the new method can be applied to both types of integral equations. Some numerical examples are given, and results are compared with other studies to...

- Numerical solution of some classes of logarithmically singular integral equations. Bhattacharya, Subhra; Mandal, B. N. // Journal of Advanced Research in Applied Mathematics;2010, Vol. 2 Issue 1, p30
In this paper, an approximate numerical method based on Bernstein polynomials is derived for solving some classes of Fredholm and Volterra integral equations with logarithmic singularities in their kernels. The method is illustrated by considering a number of integral equations. Also the...

- Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case. Agarwal, Ravi; O�Regan, Donal; Wong, Patricia // Acta Applicandae Mathematica;Sep2008, Vol. 103 Issue 3, p253
We consider the system of Fredholm integral equations and also the system of Volterra integral equations where T>0 is fixed and the nonlinearities h i ( t, u 1, u 2,..., u n ) can be singular at t=0 and u j =0 where j?{1,2,..., n}. Criteria are offered for the existence of constant-sign...

- Random Search Algorithm for Solving the Nonlinear Fredholm Integral Equations of the Second Kind. Hong, Zhimin; Yan, Zaizai; Yan, Jiao // PLoS ONE;Jul2014, Vol. 9 Issue 7, p1
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods...

- New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation. Vasin, Vladimir; Skorik, Georgy; Pimonov, Evgeny; Kuchuk, Fikri // Applied Mathematics;Nov2010, Vol. 1 Issue 5, p387
Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and...

- LOGARITHMIC COORDINATES IN INVESTIGATION OF SOLUTIONS STABILITY OF LOTKA--VOLTERRA EQUATIONS. Chernyshenko, V. S.; Belozerov, V. E. // Naukovi visti NTUU - KPI;2007, Vol. 2007 Issue 2, p148
The paper is devoted to the investigation of solutions stability of n-dimensional Lotka-Volterra system. The research wouldn't be finished successfully without using logarithmic variables. Only the first orthant was taken into consideration. All conditions were found under which the global...

- Numerical solution of Volterra integral equations with singularities. Kolk, Marek; Pedas, Arvet // Frontiers of Mathematics in China;Apr2013, Vol. 8 Issue 2, p239
The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or uniform grids, the convergence...