we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

we reduce the two phase stefan problem with kinetic to a system of nonlinear volterra integral equations of second kind and apply newton's method to linearize it. we found product integration solution of the linear form. sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

Monte Carlo integration is a widely used method to approximate high dimensional integrals. However, the randomness of this method causes the convergence to be very slow. Quasi-Monte Carlo integration uses low discrepancy sequences instead of pseudorandom sequences. The points from these sequences are more uniformly distributed. This causes the convergence to be much faster. Most research in qua...

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...