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• Open Access

ARTICLE

Approximate Analytical Solution of Time-fractional order Cauchy-Reaction Diffusion equation

H. S. Shukla1, Mohammad Tamsir1, Vineet K. Srivastava2, Jai Kumar3
CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.103.001
Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM. More >

• Open Access

ARTICLE

Space-time Discontinuous Galerkin Method Based on a New Generalized Flux Vector Splitting Method for Multi-dimensional Nonlinear Hyperbolic Systems

P.A. Trapper1, P.Z. Bar-Yoseph2
CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 19-47, 2014, DOI:10.3970/cmes.2014.103.019
Abstract The space-time discontinuous Galerkin method for multi-dimensional nonlinear hyperbolic systems is enhanced with a generalized technique for splitting a flux vector that is not limited to the homogeneity property of the flux. This technique, based on the flux’s characteristic decomposition, extends the scope of the method’s applicability to a wider range of problems, including elastodynamics. The method is used for numerical solution of a number of representative problems based on models of vibrating string and vibrating rod that involve the propagation of a sharp front through the solution domain. More >

• Open Access

ARTICLE

Solution of Two-dimensional Linear and Nonlinear Unsteady Schrödinger Equation using “Quantum Hydrodynamics” Formulation with a MLPG Collocation Method

V. C. Loukopoulos1, G. C. Bourantas2
CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 49-70, 2014, DOI:10.3970/cmes.2014.103.049
Abstract A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear… More >