Department of Mathematics and Sciences Dhofar University, Salalah Oman [email protected] Abstract Legendre wavelets methods are commonly used for the numerical solution of integral equations. In this paper, we apply the Legendre wavelets method to approximate the solution of fractional integro-differential equations. Numerical examples are also presented to demonstrate the validity of the method....

In this paper, we consider a non-autonomous stochastic LotkaVolterra competitive system dxi(t) = xi(t)[(bi(t)− n ∑ j=1 aij(t)xj(t))dt+σi(t)dBi(t)], where Bi(t) (i = 1, 2, · · · , n) are independent standard Brownian motions. Some dynamical properties are discussed and the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global at...

In this paper, the linear semiorthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations of the second kind. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computatio...

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t), . . . , xn(t))[(b(r(t)) + A(r(t))x(t))dt+ σ(r(t))dB(t)], where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction. We find out...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

In this paper, we study backward stochastic Volterra integral equations introduced in Lin [ Stochastic Anal. Appl. 20 (2002) 165–183] and Yong Process. 116 (2006) 779–795] extend the existence, uniqueness or comparison results for general filtration as Papapantoleon et al. Electron. J. Probab. 23 (2018) EJP240] (not only Brownian-Poisson setting). We also consider L p -data explore time regular...

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...