Limit and Integral Properties of Principal Solutions for Half-linear Differential Equations

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

On the Integral Characterization of Principal Solutions for Half-linear Ode

We discuss a new integral characterization of principal solutions for halflinear differential equations, introduced in the recent paper of S. Fǐsnarová and R. Mařik, Nonlinear Anal. 74 (2011), 6427–6433. We study this characterization in the framework of the existing results and we show when this new integral characterization with a parameter α is equivalent with two extremal cases of the integ...

Bernoulli collocation method with residual correction for solving integral-algebraic equations

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

A wavelet method for stochastic Volterra integral equations and its application to general stock model

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...