The Variational Methods for Solving  Random Models

Authors

  • M A Sohaly Department of Mathematics, Faculty of Science, Mansoura, Egypt Author
  • M T Yassen Department of Mathematics, Faculty of Science, Mansoura, Egypt Author

Keywords:

Random models, Second order random variable

Abstract

This paper studies the solutions of variational  methods for random ordinary (partial) dierential equations in  L2−space. These methods are called Galerkin method,  Petrov-Galerkin method, Least-Squares method and Collocation  method. Some basic properties of these methods where applying  on random problems will be shown throughout some numerical  examples.  Random models

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References

M. A. SOHALY, Mean square convergent three and five points finite difference scheme for stochastic parabolic partial differential equations, Electronic Journal of Mathematical Analysis and Applications 2 (14) (2014) 164–171.

W. Ames, Numerical Methods for Partial Differential Equations, Computer Science and Scientific Computing, Elsevier Science, 2014.

M. A. El-Tawil, M. A. Sohaly, Mean square numerical methods for initial value random differential equations,Open Journal of Discrete Mathematics 1 (2) (2011) 66–84.

J. Cortes, L. Jodar, L. Villafuerte, R. Villanueva, Computing mean square approximations of random diffusionmodels with source term, Mathematics and Computers in Simulation 76 (2007) 44–48.

M. Yassen, M. Sohaly, I. Elbaz, Random crank-nicolson scheme for random heat equation in mean square sense,American Journal of Computational Mathematics 6 (2016) 66–73.

A. Mitchell, D. Griffith, The finite difference method in partial differential equations.

J.N. Reddy, An Introduction to the Finite Element Method, Third Edition, McGraw-Hill, New York, 2006.

B. Szabo, I. Babuˇska, Finite Element Analysis, A Wiley-Interscience publication, 1991.

J. T. Oden, J. N. Reddy, Variational methods in theoretical mechanics, Springer Science & Business Media, 2012. [10] J.N. Reddy, D. K. Gartling, the finite element method in heat transfer and fluid dynamics, CRC press, 2010.

O. Zienkiewicz, R. Taylor, The Finite Element Method: Solid mechanics, Butterworth-Heinemann, 2000.

R. Wait, A. Mitchell, The Finite Element Method in Partial Differential Equations, John Willey and Sons, 1978.

C. A. J. Fletcher, Computational Galerkin Methods, Springer Berlin Heidelberg, 1984.

N. Young, An Introduction to Hilbert Space, Cambridge mathematical textbooks, Cambridge University Press,1988. [15] T. T. Soong, Random Differential Equations in Science and Engineering, Academic Press, New York, 1973.

K. Kuratowski, Topology, Elsevier Science, 2014. [17] L. Debnath, F. A. Shah, Hilbert Spaces and Orthonormal Systems, Birkh¨auser Boston, Boston, MA, 2015, pp.29–127.

R. Burden, J. Faires, Numerical Analysis, Cengage Learning, 2010.

Back Matter, ACADEMIC PRESS New York and London, 1972. doi:10.1137/1.9781611973242.bm.

J. Oden, J. Reddy, An Introduction to the Mathematical Theory of Finite Elements, Dover Books on Engineering,Dover Publications, 2012.

S. Mikhlin, The numerical performance of variational methods, Wolters-Noordho_ Series of Monographs andTextbooks on Pure and Applied Mathematics, Wolters-Noordho_ Publishing, 1971.

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Published

2024-03-04

How to Cite

The Variational Methods for Solving  Random Models. (2024). International Journal of Innovative Research in Computer Science & Technology, 5(2), 214–225. Retrieved from https://acspublisher.com/journals/index.php/ijircst/article/view/13477