Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of applying this method
to solve these problems, a comparison is made in this paper between the Newton-Kantorovich method and the
Adomian decomposition method applied to the same non-linear Sturm-Liouville problems under consideration
in this work. As a result of this comparison, the results of the Newton-Kantorovich method agreed with the
results obtained by applying Adomian’s decomposition method.
KE Sharquie, AA Noaimi, MA Al-Shukri, Journal of Cosmetics, Dermatological Sciences and Applications, 2015 - Cited by 3
In this paper, a subspace identification method for bilinear systems is used . Wherein a " three-block " and " four-block " subspace algorithms are used. In this algorithms the input signal to the system does not have to be white . Simulation of these algorithms shows that the " four-block " gives fast convergence and the dimensions of the matrices involved are significantly smaller so that the computational complexity is lower as a comparison with " three-block " algorithm .
Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef
... Show MoreA coin has two sides. Steganography although conceals the existence of a message but is not completely secure. It is not meant to supersede cryptography but to supplement it. The main goal of this method is to minimize the number of LSBs that are changed when substituting them with the bits of characters in the secret message. This will lead to decrease the distortion (noise) that is occurred in the pixels of the stego-image and as a result increase the immunity of the stego-image against the visual attack. The experiment shows that the proposed method gives good enhancement to the steganoraphy technique and there is no difference between the cover-image and the stego-image that can be seen by the human vision system (HVS), so this method c
... Show MoreThis research investigates the subject of the impact of wars (as a manifestation of crisis) on architecture, and the extent of continuing wars physical and moral results of wars, even after the end of the cause of the crisis. The impact of different rebuilding which exposed to the effects of the war seems different in crisis regions.
The problem of research is about the uncertainty of the impact of the way chooses for reconstructing the buildings after wars in the continuity of the crisis of war. The goals of this research are to clarify the influence of methods of reconstruction of buildings in a city chosen which is Beirut, on the continuation of the war crisis with the argument of demolishing and rebuilding newly or keeping tr
... Show MoreBackground: The change in the concepts of cavity preparation and the development of reliable adhesive materials lead to the development of alternative methods of caries removal. Chemo-mechanical caries removal (CMCR) involves the chemical softening of carious dentin, followed by its removal with manual excavation. The present study was conducted to evaluate clinically the efficiency of caries removal using a new chemo-mechanical agent (Papacarie) compared to the conventional drilling method in reduction of total bacterial count. Material and methods: The study is a split mouth design. The sample composes from sixty mandibular deciduous molars teeth in thirty children, between six to nine years of age with bilateral class I deep occlusal car
... Show MoreTin oxide was deposited by using vacuum thermal method on silicon wafer engraved by Computer Numerical Controlled (CNC) Machine. The inscription was engraved by diamond-made brine. Deep 0.05 mm in the form of concentric squares. Electrical results in the dark were shown high value of forward current and the high value of the detection factor from 6.42 before engraving to 10.41 after engraving. (I-V) characters in illumination with powers (50, 100, 150, 200, 250) mW/cm2 show Improved properties of the detector, Especially at power (150, 200, 250) mW/cm2. Response improved in rise time from 2.4 μs to 0.72 μs and time of inactivity improved 515.2 μs to 44.2 μs. Sensitivity angle increased at zone from 40o to 65o.