Papers by Dr. Mohammad Siddique
This paper presents a numerical comparison of third order o L stable − numerical schemes for the ... more This paper presents a numerical comparison of third order o L stable − numerical schemes for the two-dimensional parabolic partial differential equations subject to nonlocal boundary conditions. These numerical schemes are based on Pade` approximations to the matrix exponentials arising from the use of the method of lines and are tested on a model problem. The numerical comparison shows that the (0, 3)-Padé scheme is efficient and provide very accurate results as compared to (1, 2)-Padé scheme.
Parabolic partial differential equation with nonlocal boundary conditions arise in modeling of va... more Parabolic partial differential equation with nonlocal boundary conditions arise in modeling of various physical phenomena in areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper deals with the successful implementation of the positively smoothed Pade` schemes (PSP) to two-dimensional parabolic partial differential equations with nonlocal boundary conditions. We considered both Homogeneous and Inhomogeneous cases. The numerical results show that these numerical schemes are quite accurate.
Proceedings of the 2010 American Conference on Applied Mathematics, Jan 27, 2010
Parabolic partial differential equation with nonlocal boundary conditions arise in modeling of va... more Parabolic partial differential equation with nonlocal boundary conditions arise in modeling of various physical phenomena in areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper deals with the successful implementation of Rannacher 's smoothing scheme to two-dimensional inhomogeneous parabolic partial differential equations with nonlocal boundary conditions under nonsmooth data situation. The graphical results show an excellent smoothing and numerical results prove the accuracy of these smoothing schemes.
Smoothing of Crank-Nicolson Method for 2-D Inhomogeneous Parabolic Problems with Nonlocal Boundary Conditions
2009 WRI World Congress on Computer Science and Information Engineering, 2009
Parabolic partial differential equations with nonlocal boundary conditions have important applica... more Parabolic partial differential equations with nonlocal boundary conditions have important applications in chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper is concerned with the smoothing of Crank-Nicolson numerical scheme for two-dimensional parabolic partial differential equations with nonlocal boundary conditions. The graphs of smoothing of the Crank-Nicolson scheme are presented. The absolute relative error before and
Smoothing of Crank-Nicolson Method for 2-D Inhomogeneous Parabolic Problems with Nonlocal Boundary Conditions
2009 WRI World Congress on Computer Science and Information Engineering, 2009
Parabolic partial differential equations with nonlocal boundary conditions have important applica... more Parabolic partial differential equations with nonlocal boundary conditions have important applications in chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper is concerned with the smoothing of Crank-Nicolson numerical scheme for two-dimensional parabolic partial differential equations with nonlocal boundary conditions. The graphs of smoothing of the Crank-Nicolson scheme are presented. The absolute relative error before and
Smoothing with positivity‐preserving Padé schemes for parabolic problems with nonsmooth data
We introduce a new class of higher order numerical schemes for parabolic partial differential equ... more We introduce a new class of higher order numerical schemes for parabolic partial differential equations that are more robust than the well-known Rannacher schemes. The new family of algorithms utilizes diagonal Pade schemes combined with positivity-preserving Pade schemes instead of first subdiagonal Pade schemes. We utilize a partial fraction decomposition to address problems with accuracy and computational efficiency in solving the higher order methods and to implement the algorithms in parallel. Optimal order convergence for nonsmooth data is proved for the case of a self-adjoint operator in Hilbert space as well as in Banach space for the general case. Numerical experiments support the theorems, including examples in pricing options with nonsmooth payoff in financial mathematics. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
Mathematical Concepts and Maple Animations
Maple is a mathematics software package, which contains graphic, computation, and programming too... more Maple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subject.
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Papers by Dr. Mohammad Siddique