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008			210914s2021 ua dh f m 000 0 eng d
040			_aEG-GiCUC _beng _cEG-GiCUC
041	0		_aeng
049			_aDeposite
097			_aPh.D
099			_aCai01.12.17.Ph.D.2021.Ma.N
100	0		_aMaha Muftah Almuttardi
245	1	0	_aNumerical studies for various random and stochastic differential equations / _cMaha Muftah Almuttardi ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Doaa M. Elsakout
246	1	5	_aدرا{uئإآ٣}{uئإ٨إ}ت {uئإأآ}{uئإءء}د{uئآئإ}{uئإ٩٤} {uئإؤئ}{uئإ٩٢}{uئإأأ}{uئإآإ} ا{uئإؤئ}{uئإإ٤}{uئإأأ}{uئإ٨إ}د{uئإئآ}ت ا{uئإؤئ}{uئإ٩٨}{uئإؤ٤}{uئإ٨إ}{uئإآئ}{uئإإ٠}{uئآئئ}{uئإ٩٤} ا{uئإؤئ}{uئإأأ}{uئإآ٨}{uئإإإ}ا{uئإ٨آ}{uئآئئ}{uئإ٩٤}
260			_aCairo : _bMaha Muftah Almuttardi , _c2021
300			_a247 P. : _bcharts , facsimiles ; _c25cm
502			_aThesis (h.D.) - Cairo University - Faculty of Science - Department of Mathematics
520			_aStochastic partial differential equations become very powerful extensions of deter- ministic partial differential equations. Under appropriate assumptions, the existence and uniqueness of solutions to such equations are ensured. However, in many cases, these solutions are not given explicitly, therefore the numerical approximations are used to study the properties of these models. The theme of this thesis is numerical studies for solving certain partial differential equations involving uncertainties.These uncertainties arise in the form of forcing terms or initial data. We convert the underlying stochastic partial differential equations into stochastic ordinary differential equations by discretizing the spatial in spatial direction. We then solving the new resultant stochastic ordinary differential equations using dif- ferent scenarios.That scenarios are Euler-Maryuma procedure, method of lines and high-order ordinary differential equations solver. To evaluate uncertainty in the calcu- lations, we estimate the expectation by using repeated generators of random numbers. We then obtaining different sample paths, and considering the expectation. When the number of samples grows, the predicted estimated value converges to the true estimate.The idea behind this study is: to enhanced the performance of the deterministic numerical methods when it is used on stochastic models, analyze similarities between the exact solution and numerical approximations for different sample paths and accel- erate the convergence rate of the solutions.The main contributions in this thesis, we obtained more accurate numerical solutions for more general models, captured real physical phenomena not easily obtained in deterministic cases and we accelerated the convergence rate. The thesis handles the space fractional version of the Stochastic Advection-Diffusion Equation using the stochastic compact {uFB01}nite difference scheme
530			_aIssued also as CD
653		4	_aNumerical studies
653		4	_aStochastic differential equations
653		4	_aVarious random
700	0		_aDoaa M. Elsakout , _eSupervisor
700	0		_aLaila F. Abdelal , _eSupervisor
700	0		_aNasser H. Sweilam , _eSupervisor
856			_uhttp://172.23.153.220/th.pdf
905			_aNazla _eRevisor
905			_aShimaa _eCataloger
942			_2ddc _cTH
999			_c82135 _d82135