http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1122 Tue, 07 Apr 2026 05:30:23 GMT 2026-04-07T05:30:23Z http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1187 Numerical convergence of a one step approximation of an integro-differential equation Bhowmik, Samir Kumar We consider a linear partial integro-differential equation that arises in modeling various physical and biological processes. We study the problem in a spatial periodic domain. We analyze numerical stability and numerical convergence of a one step approximation of the problem with smooth and non-smooth initial functions. Fri, 17 Aug 2012 00:00:00 GMT http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1187 2012-08-17T00:00:00Z http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1186 Finite to Infinite Steady State Solutions, Bifurcations of an Integro-Differential Equation Bhowmik, Samir K.; Duncan, Dugald B.; Grinfeld, Michael; Lord, Gabriel J. We consider a bistable integral equation which governs the sta- tionary solutions of a convolution model of solid–solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is increased to examine the transition from an uncountably infinite number of steady states to three for the continuum limit of the semi– discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem. Fri, 01 Jul 2011 00:00:00 GMT http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1186 2011-07-01T00:00:00Z http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1185 Numerical approximation of a convolution model of ˙ θ-neuron networks Bhowmik, Samir Kumar In this article, we consider a nonlinear integro-differential equation that arises in a ˙ θ-neural networks modeling. We analyze boundedness and invertibility of the model operator, construct approximate solutions using piecewise polynomials in space, and estimate the theoretical convergence rate of such spatial approximations. We present some numerical experimental results to demonstrate the scheme. Wed, 22 Dec 2010 00:00:00 GMT http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1185 2010-12-22T00:00:00Z http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1184 Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations Bhowmik, Samir K.; Stolk, Christiaan C. We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given by the symbol of the PDO evaluated at the wave number and central position of the windowed plane wave. This can be exploited in a preconditioning method for use in iterative inversion. For domains with periodic boundary conditions we find that the condition number with the preconditioning becomes bounded and the iteration converges well. For problems with a Dirichlet boundary condition, some large and small singular values remain. However the iterative inversion still appears to converge well. Thu, 17 Feb 2011 00:00:00 GMT http://reposit.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1184 2011-02-17T00:00:00Z