Prabir Daripa

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Fast algorithms for the accurate evaluation of some singular integral operators that arise in the context of solving certain partial differential equations within the unit circle in the complex plane are presented. These algorithms are generalizations and extensions of a fast algorithm of Daripa [11]. They are based on some recursive relations in Fourier(More)
We consider an ill-posed Boussinesq equation which arises in shallow water waves and nonlinear lattices. This equation has growing and decaying modes in the linear as well as nonlinear regimes and its linearized growth rate r for short-waves of wavenumber k is given by r k. Previous numerical studies have addressed numerical diculties and construction of(More)
The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [Jour. Comput. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible(More)
The linear stability of three-layer Hele–Shaw flows with middle-layer having variable viscosity is considered. Based on application of the Gerschgorin s theorem on finite-difference approximation of the linearized disturbance equations, an upper bound of the growth rate is given and its limiting case for the case of constant viscosity middle-layer is(More)
A class of model equations that describe the bi-directional propagation of small amplitude long waves on the surface of shallow water is derived from two-dimensional potential flow equations at various orders of approximation in two small parameters, namely the amplitude parameter α = a/h0 and wavelength parameter β = (h0/l) , where a and l are the actual(More)
A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a different(More)
We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. This method can be easily extended to three-dimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which the arbitrary domain is embedded. A periodic solution of the(More)