Linear and Nonlinear Integral Equations pp Cite as.
It was stated in Chapter 2 that Volterra integral equations arise in many scientific applications such as the population dynamics, spread of epidemics, and semi-conductor devices. It was also shown that Volterra integral equations can be derived from initial value problems. Volterra started working on integral equations in , but his serious study began in The name sintegral equation was given by du Bois-Reymond in However, the name Volterra integral equation was first coined by Lalesco in Unable to display preview.
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Download preview PDF. Pedas, G. Vainikko, The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations, Math. Diogo, A note on collocation and iterated collocation methods for a class of weakly singular Volterra integral equations, submitted.
Diogo, N. Franco, P. Lima, High order product integration methods for a Volterra integral equation with logarithmic singular kernel, Commun.
Pure Appl. Diogo, P. Lima, Superconvergence properties of collocation methods for a Volterra integral equation with weakly singular kernel, to appear in J. Diogo, S.
McKee, T. Tang, A Hermite-type collocation method for the solution of an integral equation with a certain weakly singular kernel, IMA J.
Mckee, T. Tang, Collocation methods for second-kind Volterra integral equations with weakly singular kernels, Proc. Edinburgh, A , Galperin, E.
Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations.
Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. The model equations are made explicit for diodes, transistors and thyristors. The integral equation model allows to recover all relevant properties of the voltage—current characteristics.
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