Browsing by Author "Molati, M."
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Item Direct approach to a group classification problem: Fisher equation with time-dependent coefficients(World Scientific Publishing, 2016) Molati, M.; Khalique, C. M.We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations.Item An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems(SPEKTRUM STU Publishing, 2017-12-29) Molati, M.; Murakawa, H.This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages, namely, it is very easy-to-implement, the ensuing linear algebraic systems are symmetric, it requires low computational cost, the accuracy is comparable to that of the well-studied nonlinear schemes, the computation is much faster than the nonlinear schemes to obtain the same level of accuracy. In this paper, numerical experiments are carried out to demonstrate efficiency of the proposed scheme.Item Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry analysis approach(Elsevier, 2019) Molati, M.; Murakawa, H.We derive some exact solutions of a nonlinear diffusion-convection-reaction equation which models biological, chemical and physical phenomena. The Lie symmetry classification approach is employed to specify the model parameters and then the symmetries of resulting submodels are utilized for construction of exact solutions.Item Group classification, symmetry reductions and exact solutions of a generalized Korteweg-de Vries-Burgers equation(Natural Sciences Publishing, 2015-01-01) Molati, M.; Khaliqu, C. M.; Adem, A.R.Lie group classification is performed on the generalized Korteweg-de Vries-Burgers equationut+δuxxx+g(u)ux−νuxx+γu=f(x), which occurs in many applications of physical phenomena. We show that the equation admits a four-dimensional equivalenceLie algebra. It is also shown that the principal Lie algebra consists of a single translation symmetry. Several possibleextensions of theprincipal Lie algebra are computed and their associated symmetry reductions and exact solutions are obtained. Also, one-dimensionaloptimal system of subalgebras is obtained for the case when the principal Lie algebra is extended by two symmetries.Item Lie Group Analysis of a Forced KdV Equation(Hindawi Publishing Corporation, 2013) Molati, M.; Khalique, C. M.Item Symmetry classification and invariant solutions of the variable coefficient BBM equation(Elsevier, 2013) Molati, M.; Khalique, C. M.We perform Lie symmetry classification of a time-variable coefficient BBM equation, which arises in the modeling of long waves of small amplitude in �1 � 1� dimensions. The direct method of group classification is employed to specify the forms of these time-dependent coefficients. Some exact solutions are derived.Item Symmetry classification of coupled heat-diffusion systems via low dimensional Lie algebras(World Scientific Publishing, 2013) Mahomed, F.M.; Molati, M.We review second-order system of coupled heat-diffusion equations. The system under consideration contains several arbitrary elements the forms of which are specified via the method of group classification based on the use of low-dimensional Lie algebras. We collect and present several results.