Abstract In this thesis, we study different numerical methods used to solve ordinary differential equations of the first and second orders and where related important definitions are given . We will concentrate first on Differential Equations of the first order and the truncation errors which are derived for various methods and those compared with the expected errors , whenever possible . Two applications were given in science of biology and physics which were studied in details . Finally we draw our attention to ordinary differential equations of the second order where we study initial-value problems and boundary-value problems with the application of the wellknown numerical procedures :the shooting method and the finite difference method . The important conclusion we came up with is that the truncation error is always greater than the expected error for all methods used, and this which was expected .
عفاف احمد الجطلاوي (2014)

حل مسالة القيمة الذاتية للنمطين الكهربي TE و المغناطيسي TM المستعرضين لالفالم الرقيقة دورية الطبقات. arabic 241 English 4
عبدالسلام إمحمد إبراهيم ابوبكر, عبدالعزيز أحمد الكويلاني, علي امحمد بشير المجاهد(7-2019)

Abstract The basaltic Intrusions of the Central Jabal Nafūsah Foothills which extend from NW Wādi Zāret to NE Wādi Ghān Dām are part of the latest stage of Gharyān Volcanic Province (GVP). These intrusions are classified on basis of their shape and mechanism of emplacement into four kinds of volcanic bodies. These are; sheets (dykes and a sill), dykes associated with volcaniclasts, volcanic cone and lava mounds. Generally, the dyke emplacements are restricted only to the area between Wādi Zāret to Abū Ghaylān, while the other forms extend from Rās al Mazūl Dome to Wādi Ghān Dam. The more differentiated rocks are restricted to the area between Rās al Mazūl Dome and Wādi Ghān. Farther west towards Wādi Zāret, ultramafic xenoliths and magnesium-number increase, suggesting closer proximity to the source. The rocks are essentially alkaline with within Intraplate signatures. They straddle the composition from picrites, basanites, alkali basalts through hawaiites, mugearite to benmoreites with a compositional gap between the last two types. Generally, the phenocrysts are represented by foresteritic olivine, Cadiopsidic pyroxene, magnesiotaramitic amphibole, plagioclase, K-feldspar and titanomagnetite. The chemical composition of the mafic minerals indicates that they are high pressure phenocryst phases. The most primitive picrites satisfied the criteria of primary mantle melts. The rocks are generally, enriched in LILE suggesting an enriched mantle source. The studied rocks were grouped into five groups based on incompatible trace element ratios; Group-A includes picrite, basanites and hawaiites, and Group-B includes picrite (Z-3), basanites , alkali basalts, and hawaiites, while Group-C is formed of hawaiites, Group-D is composed of mugearite and Group-E is made up of benmoreites. Picrites and basanites of these rock have high Mg-number (>0.64), high Cr and Ni contents and strong light rare earth element enrichment, but systematic depletion in Rb, K and Ba relative to trace elements of similar compatibility in anhydrous mantle. Alkali basalts and more differentiated magmatic rocks have lower Mg-number and lower abundances of Ni and Cr, and have undergone fractionation of mainly olivine, clinopyroxene, Fe–Ti oxide, amphibole and plagioclase. The variation in the concentrations of major, trace, rare earth elements, and incompatible element ratios in the rock samples demonstrate the heterogeneous character of their source region. Such heterogeneity can be interpreted by the involvement of a heterogeneous mantle reservoir to different degrees of partial melting. The REE data require residual spinel stability peridotite field in the source and constrain the melting process of Group-C and Group-D to 2% to 3.5% degrees of melting respectively, Group-A and Group-B both to 5% degree of partial melting while Group-E to 10% degree of partial melting of spinel lherzolite xenoliths of Al Ourban area. Mass balance modelling of the major suggests two possible FC scenarios; Derivation of basanites and hawaiites of group-A from G-3 picritic parental magma. Derivation of Group-D and Group-E was also possible from these basanites. Derivation of basanites of Group-B from Z-3 picrite parental magma and simultaneous derivation of G-4 and QJ-1 alkali basalts from Z-3 picrite parental magma. V Simple mass-balance calculations suggest that the melting assemblages of picrites and basanites consisted of forsteritic olivine, diopsidic clinopyroxene, Ti-magnetite. While the alkali basalts and more differentiated magmatic rocks, mass-balance calculations suggest that the melting assemblages consisted of sodic plagioclase, magnesiotaramitic amphibole, diopsidic pyroxene, Ti-magnetite, K-feldspar with sub amounts of apatite and sphene.
سمية عون (2015)