A new numerical method, based on the normalized Bernstein polynomials for solving singular integral equations of Abel type is presented here in this paper. We construct an othonormal family { } i n i b 0 = of polynomials of degree n from the th n degree Bernstein polynomials n i B and use them as a basis to approximate the known and unknown functions ) (x f and ) (x φ respectively in the Abel’s...

In this work, we consider rational ordinary differential equations dy/dx = Q(x, y)/P (x, y), with Q(x, y) and P (x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for which a first integral can be expressed from two independent solutions of a second–order homogeneous linear differential equation. This first integral is, in general, given by a...

The nonlinear integral equations arise in the theory of parabolic boundary value problems, engineering, various mathematical physics, and theory of elasticity 1–3 . In recent years, several analytical and numerical methods of this kind of problems have been presented 4, 5 . Analytically, the decomposition methods are used in 6, 7 . The classical method of successive approximations was introduce...

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are ...

In this article we prove two new criteria for the existence of rational general integral of an algebraic differential equation (cf. [4]) on the complex projective plane. These results are stated in terms of divisors and zero-cycles of a projective variety and are built by using intersection numbers of projective curves and multiplicities of singularities. We also prove a new result giving new s...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In the 1970s, William Tutte developed a clever algebraic approach, based on certain "invariants", to solve functional equation that arises in enumeration of properly colored triangulations. The plane lattice walks confined first quadrant is governed by similar equations, and has led past 20 years rich collection attractive results dealing with nature (algebraic, D-finite or not) associated gene...

In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal f...

This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices integration based on Hybridization block-pulse and Taylor polynomials are implemented to transform these equations into a system linear algebraic error analysis proposed method is examined in detail. Numerical results highlight robustn...