Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity fluid, property responsible various flow instabilities major modifications fluid dynamics. Recent developments numerical methods simulation viscoelastic flows, described by continuum-level differential cons...

Through introducing a new iterative formula for divided difference using Neville's and Aitken's algorithms, we study new iterative methods for interpolation, numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evenly or unevenly spaced data. Basic computer algorithms for new methods are given.

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...

Fixed step, symmetric Runge-Kutta-Nyström formulae have proved to be very efficient for the numerical integration of a large class of reversible second order systems of ordinary differential equations of the special form d 2y dt2 = f(t, y). However for some important classes of problems it is necessary, for the sake of efficiency, to allow a variable steplength of integration to be used and in ...