Faculty of Science http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/16 2020-02-20T11:12:10Z Studies on Eigenvalue Analysis for a Class of Differential Equations by the Methods of Weighted Residuals http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1545 Studies on Eigenvalue Analysis for a Class of Differential Equations by the Methods of Weighted Residuals Farzana, Humaira This thesis submitted for the degree of Doctor of Philosophy in The University of Dhaka. 2019-12-10T00:00:00Z Numerical convergence of a one step approximation of an integro-differential equation http://repository.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. 2012-08-17T00:00:00Z Finite to Infinite Steady State Solutions, Bifurcations of an Integro-Differential Equation http://repository.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. 2011-07-01T00:00:00Z Numerical approximation of a convolution model of ˙ θ-neuron networks http://repository.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. 2010-12-22T00:00:00Z