A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is test...

The paper extends the use of multichannel filtered-x affine projection algorithms suitable for feed-forward active noise control to a broad class of nonlinear filter structures, which comprises also Volterra filters and Functional Link Artificial Neural Networks (FLANN). An analysis of the transient and steady-state behavior of the resulting algorithms is provided. Some experimental results tha...

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive fo...

Nonlinear distortions and memory effect of broadband receiver’s front-end are canceled out simultaneously using a digital post-calibration technique based on Volterra model. This paper develops a least mean squared blind identification criterion for the measurement of the model parameters without prior knowledge of the received signals, and the optimization goal could be described as for the mi...

Detecting nonlinear correlations between time series presents a hard problem for data analysis. We present a generative statistical modeling method for detecting nonlinear generalized synchronization. Truncated Volterra series are used to approximate functional interactions. The Volterra kernels are modeled as linear combinations of basis splines, whose coefficients are estimated via l(1) and l...

Acoustic echo cancellers in today' s speakerphones or video conferencing systems rely on the assumption of a linear echo path. Low-cost audio equipment or constraints of portable communication systems cause nonlinear distortions, which limit the echo return loss enhancement achievable by linear adaptation schemes. These distortions are a superposition of different effects, which can be modelled...

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.

ii ACKNOWLEDGEMENT No volume of words is enough to express my gratitude towards my guide, Thapar University, who has been very concerned and has aided for all the material essential for the preparation of this thesis report. He has helped me to explore this vast topic in an organized manner and provided me with all the ideas on how to work towards a research-oriented venture. for the motivation...