-
Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation
Rabab Ahmed Shanab,
Laila Fouad Seddek,
Salwa Amin Mohamed
Issue:
Volume 2, Issue 3, June 2013
Pages:
64-77
Received:
13 May 2013
Published:
30 June 2013
Abstract: In this paper, we extend the work of Kalita et al. [11] to solve the steady 3D convection-diffusion equation with variable coefficients on non-uniform grid. The approach is based on the use of Taylor series expansion, up to the fourth order terms, to approximate the derivatives appearing in the 3D convection diffusion equation. Then the original convection-diffusion equation is used again to replace the resulting higher order derivative terms. This leads to a higher order scheme on a compact stencil (HOC) of nineteen points. Effectiveness of this method is seen from the fact that it can handle the singularity perturbed problems by employing a flexible discretized grid that can be adapted to the singularity in the domain. Four difficult test cases are chosen to demonstrate the accuracy of the present scheme. Numerical results show that the fourth order accuracy is achieved even though the Reynolds number (Re) is high.
Abstract: In this paper, we extend the work of Kalita et al. [11] to solve the steady 3D convection-diffusion equation with variable coefficients on non-uniform grid. The approach is based on the use of Taylor series expansion, up to the fourth order terms, to approximate the derivatives appearing in the 3D convection diffusion equation. Then the original co...
Show More
-
Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations
Issue:
Volume 2, Issue 3, June 2013
Pages:
78-85
Received:
18 May 2013
Published:
30 June 2013
Abstract: The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations.
Abstract: The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) in this paper. The effective...
Show More
-
A Note on Self Complementary Brittle and Self Complementary Quasi Chordal Graphs
Parvez Ali,
Merajuddin,
Syed Ajaz Kareem Kirmani
Issue:
Volume 2, Issue 3, June 2013
Pages:
86-91
Received:
2 June 2013
Published:
20 July 2013
Abstract: In this paper we deal with some classes of self-complementary (sc) perfectly orderable graphs namely sc brittle, sc quasi chordal graphs and propose algorithms for these classes. We obtain some results on these classes and an algorithm is proposed based on these results that recognize these classes. We also compile a catalogue for these classes up to 17 vertices.
Abstract: In this paper we deal with some classes of self-complementary (sc) perfectly orderable graphs namely sc brittle, sc quasi chordal graphs and propose algorithms for these classes. We obtain some results on these classes and an algorithm is proposed based on these results that recognize these classes. We also compile a catalogue for these classes up ...
Show More
-
Assessment of Earth Surface Pollution due to Residual Rocket Fuel
Zhumagulov Bakhytzhan,
Abdibekov Ualikhan,
Karzhaubayev Kairzhan,
Khikmetov Askar,
Zhubat Kuanysch
Issue:
Volume 2, Issue 3, June 2013
Pages:
92-95
Received:
18 June 2013
Published:
20 July 2013
Abstract: This paper presents aerohydrodynamic modeling of air and surface pollution caused by toxic rocket fuel components. A numerical algorithm for solving this problem was developed and implemented in a software code in FORTRAN. Modeling of the dissimilation of rocket fuel dynamics for the case of the second-stage rocket "Proton-M" emergency fall was carried out using the developed software package. Finally, the modeling results were compared with a map of vegetation cover contamination in the region of the carrier-rocket second-stage fall.
Abstract: This paper presents aerohydrodynamic modeling of air and surface pollution caused by toxic rocket fuel components. A numerical algorithm for solving this problem was developed and implemented in a software code in FORTRAN. Modeling of the dissimilation of rocket fuel dynamics for the case of the second-stage rocket "Proton-M" emergency fall was car...
Show More
-
Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation
Ilgar Gurbat oglu Mamedov
Issue:
Volume 2, Issue 3, June 2013
Pages:
96-99
Received:
24 June 2013
Published:
20 July 2013
Abstract: In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) .
Abstract: In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (he...
Show More
