The equation for the orbit of the classical Lotka-Volterra oscillator is solved for one of two variables in terms of the other by using two inverse functions of x exp(x). Moreover, the period of the orbit is expressed as an integral, which is approximated numerically by Gauss-Tschebyscheff integration rule of the first kind.

A cubic spline approximation in C1 to the solution of a general Volterra integral equation of the second kind is constructed. Under certain conditions, convergence of the approximation and its first two derivatives is proved and error bounds are obtained. The question of stability is not examined.

in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.

We study the nonhogeneous heat equation under the form: u t ? u xx = '(t)f(x), where the unknown is the pair of functions (u; f). Under various assumptions about the the function ' and the nal value in t = 1 i.e. g(x), we propose diierent regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For ' 6 6 0 the solution is unique. I. Introducti...

E-Methnds for .,aflving linear Volterra integral equatitms of the first kind with smot~th kernels are considered. E-MethotL~ are a new type of numerical algorithms computing numerical approximations together with mathematically guaranteed do.~ error I~amds, The basic concepts from verifi~ttion thet~ry are sketched and such ~lf-validating numerics derived. O~mputati~mal experiments show the effi...

The basic linear, Volterra integral equation of the first kind with a weakly singular kernel is solved via a Galerkin approximation. It is shown that the approximate solution is a sum with the first term being the solution of Abel's equation and the remaining terms computable as components of the solution of an initialvalue problem. The method represents a significant decrease in the normal num...

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...