# HYBRID METHODS FOR SOLVING VOLTERRA INTEGRAL EQUATIONS

## Related Articles

- HYBRID METHODS FOR SOLVING VOLTERRA INTEGRAL EQUATIONS. MEHDIYEVA, GALINA; IMANOVA, MEHRIBAN; IBRAHIMOV, VAGIF // Journal of Concrete & Applicable Mathematics;Apr2013, Vol. 11 Issue 2, p246
It is known that there exists a class of methods for solving integral equations with variable boundary. One of them is the most popular methods of quadratures. This method is clarified and modified by many scientists. Here, to numerically solving Volterra integral equations the hybrid method is...

- On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation. Mamba, H. S.; Khumalo, M. // Abstract & Applied Analysis;2014, p1
We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the...

- L solutions of backward stochastic Volterra integral equations. Wang, Tian // Acta Mathematica Sinica;Sep2012, Vol. 28 Issue 9, p1875
This paper is devoted to the unique solvability of backward stochastic Volterra integral equations (BSVIEs, for short), in terms of both M-solution and the adapted solutions. We prove the existence and uniqueness of M-solutions of BSVIEs in L (1 < p < 2), which extends the existing results on...

- Integral Solutions of kxy - w(x + y) = zï¿½. Gopalan, M. A.; Vidhyalakshmi, S. // Advances in Theoretical & Applied Mathematics;2006, Vol. 1 Issue 2, p167
We search for non-zero integer quadruples (x, y, z, w) satisfying the quadratic equation kxy - w(x + y) = zï¿½. The recurrence relations for the solutions are presented. Given a solution, a general formula for the generation of solutions is also obtained.

- On Bivariate Quadratic Equation kxy + 2m(x + y) = xï¿½ - yï¿½. Gopalan, M. A.; Vidhyalakshmi, S. // Advances in Theoretical & Applied Mathematics;2006, Vol. 1 Issue 2, p163
Non-trivial integral solutions of the bivariate quadratic equation kxy + 2m(x + y) = xï¿½-yï¿½, (k, m ? 0) are obtained. Recurrence relations for x,y are given. Interesting results among the solutions are presented.

- Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind. Avazzadeh, Zakieh; Heydari, Mohammad // Computational & Applied Mathematics;2012, Vol. 31 Issue 1, p127
In this paper, an efficient method is presented for solving two dimensional Fred-holm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations...

- An Optimized Two-step Hybrid Block Method for Solving General Second Order Initial-value Problems of the Form y" = Âƒ(x, y, y'). Ramos, Higinio; Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. // AIP Conference Proceedings;2015, Vol. 1648 Issue 1, p1
In this paper, an efficient new optimized implicit two-step hybrid block method is presented for the integration of general second-order initial value problems. Numerical experiments reveal the superiority of the new method for solving this kind of problems, in comparison with methods of similar...

- Eigenvalues and eigenfunctions of the Gellerstedt problem for the multidimensional Lavrent'ev-Bitsadze equation. Aldashev, S. // Ukrainian Mathematical Journal;Nov2011, Vol. 63 Issue 6, p962
We determine eigenvalues and eigenfunctions of the Gellerstedt problem for the multidimensional Lavrent'ev-Bitsadze equation.

- Modification of a method of generalized separation of variables for the solution of multidimensional integral equations. Biletskyy, V. // Journal of Mathematical Sciences;Mar2012, Vol. 181 Issue 3, p340
We describe a method of generalized separation of variables for the solution of multidimensional integral equations and its modification minimizing the deviation of an approximate solution from the exact one. The convergence of the modified method is proved. A comparison of methods on the basis...