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Journals and Conferences
A linear partial integro-differential equation is solved both numerically and analytically using variational iteration method. This equation typically arises in viscoelasticity and other areas. The analytic solution is represented by an infinite series.
For a given nonzero bounded linear operator A on a Banach space X, we show that if A or A∗ has an eigenvalue then, except when the dimension of X is equal to two and the trace of A is zero, there exists a bounded linear operator B on X such that (i) AB + BA is of rank one, and (ii) I + f (A)B is invertible for every function f analytic in a neighborhood of… (More)
Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.
We consider an optimal control problem of a system of parabolic partial differential equations modelling the competition between an invasive and a native species. The motivating example is cottonwood-salt cedar competition, where the effect of disturbance in the system (such as flooding) is taken to be a control variable. Flooding being detrimental at low… (More)
An optimal control of a two dimensional time dependent thermistor problem is considered. The problem consists of two nonlinear partial differential equations coupled with appropriate boundary conditions which model the coupling of the thermistor to its surroundings. Based on physical considerations, an objective functional to be minimized is introduced and… (More)
Pierce's disease (PD) is a fatal disease of grapevines which results from an infection by the plant pathogen Xyllela fastidiosa. This bacterium grows in the xylem (water-conducting) vessels of the plant blocking movement of water. PD can kill vines in one year and poses a serious threat to both the California and the expanding Texas wine industries.… (More)