Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8

Search results for: Sandile S. Motsa

8 An Optimal and Efficient Family of Fourth-Order Methods for Nonlinear Equations

Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

Abstract:

In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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7 Semilocal Convergence of a Three Step Fifth Order Iterative Method under Hölder Continuity Condition in Banach Spaces

Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

Abstract:

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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6 Sixth-Order Two-Point Efficient Family of Super-Halley Type Methods

Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: basins of attraction, nonlinear equations, simple roots, super-Halley

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5 The Review for Repair of Masonry Structures Using the Crack Stitching Technique

Authors: Sandile Daniel Ngidi

Abstract:

Masonry structures often crack due to different factors, which include differential movement of structures, thermal expansion, and seismic waves. Retrofitting is introduced to ensure that these cracks do not expand to a point of making the wall fail. Crack stitching is one of many repairing methods used to repair cracked masonry walls. It is done by stitching helical stainless steel reinforcement bars to reconnect and stabilize the wall. The basic element of this reinforcing system is the mechanical interlink between the helical stainless-steel bar and the grout, which makes it such a flexible and well-known masonry repair system. The objective of this review was to use previous experimental work done by different authors to check the efficiency and effectiveness of using the crack stitching technique to repair and stabilize masonry walls. The technique was found to be effective to rejuvenate the strength of a masonry structure to be stronger than initial strength. Different factors were investigated, which include economic features, sustainability, buildability, and suitability of this technique for application in developing communities.

Keywords: brickforce, crack-stitching, masonry concrete, reinforcement, wall panels

Procedia PDF Downloads 47
4 The Optimal Location of Brickforce in Brickwork

Authors: Sandile Daniel Ngidi

Abstract:

A brickforce is a product consisting of two main parallel wires joined by in-line welded cross wires. Embedded in the normal thickness of the brickwork joint, the wires are manufactured to a flattened profile to simplify location into the mortar joint without steel build-up problems at lap positions corners/junctions or when used in conjunction with wall ties. A brickforce has been in continuous use since 1918. It is placed in the cement between courses of bricks. Brickforce is used in every course of the foundations and every course above lintel height. Otherwise, brickforce is used every fourth course in between the foundations and lintel height or a concrete slab and lintel height. The brickforce strengthens and stabilizes the wall, especially if you are building on unstable ground. It provides brickwork increased resistance to tensional stresses. Brickforce uses high tensile steel wires, which can withstand high forces but with a very little stretch. This helps to keep crack widths to a minimum. Recently a debate has opened about the purpose of using brickforce in single-story buildings. The debate has been compounded by the fact that there is no consensus about the spacing of brickforce in brickwork or masonry. In addition, very little information had been published on the relative merits of using the same size of brickforce for the different atmospheric conditions in South Africa. This paper aims to compare different types of brickforce systems used in different countries. Conclusions are made to identify the point and location of brickforce that optimize the system.

Keywords: brickforce, masonry concrete, reinforcement, strengthening, wall panels

Procedia PDF Downloads 125
3 Woody Plant Encroachment Effects on the Physical Properties of Vertic Soils in Bela-Bela, Limpopo Province

Authors: Rebone E. Mashapa, Phesheya E. Dlamini, Sandile S. Mthimkhulu

Abstract:

Woody plant encroachment, a land cover transformation that reduces grassland productivity may influence soil physical properties. The objective of the study was to determine the effect of woody plant encroachment on physical properties of vertic soils in a savanna grassland. In this study, we quantified and compared soil bulk density, aggregate stability and porosity in the top and subsoil of an open and woody encroached savanna grassland. The results revealed that soil bulk density increases, while porosity and mean weight diameter decreases with depth in both open and woody encroached grassland soil. Compared to open grassland, soil bulk density was 11% and 10% greater in the topsoil and subsoil, while porosity was 6% and 9% lower in the topsoil and subsoil of woody encroached grassland. Mean weight diameter, an indicator of soil aggregation increased by 38% only in the subsoil of encroached grasslands due to increasing clay content with depth. These results suggest that woody plant encroachment leads to compaction of vertic soils, which in turn reduces pore size distribution.

Keywords: soil depth, soil physical properties, vertic soils, woody plant encroachment

Procedia PDF Downloads 61
2 Magnetohydrodynamic Flow of Viscoelastic Nanofluid and Heat Transfer over a Stretching Surface with Non-Uniform Heat Source/Sink and Non-Linear Radiation

Authors: Md. S. Ansari, S. S. Motsa

Abstract:

In this paper, an analysis has been made on the flow of non-Newtonian viscoelastic nanofluid over a linearly stretching sheet under the influence of uniform magnetic field. Heat transfer characteristics is analyzed taking into the effect of nonlinear radiation and non-uniform heat source/sink. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into ordinary differential equations by using appropriate similarity transformations. The transformed, highly nonlinear, ordinary differential equations are solved by spectral local linearisation method. The numerical convergence, error and stability analysis of iteration schemes are presented. The effects of different controlling parameters, namely, radiation, space and temperature-dependent heat source/sink, Brownian motion, thermophoresis, viscoelastic, Lewis number and the magnetic force parameter on the flow field, heat transfer characteristics and nanoparticles concentration are examined. The present investigation has many industrial and engineering applications in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Keywords: magnetic field, nonlinear radiation, non-uniform heat source/sink, similar solution, spectral local linearisation method, Rosseland diffusion approximation

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1 The Effect of Hydroxyl Ethyl Cellulose (HEC) and Hydrophobically-Modified Alkali Soluble Emulsions (HASE) on the Properties and Quality of Water Based Paints

Authors: Haleden Chiririwa, Sandile S. Gwebu

Abstract:

The coatings industry is a million dollar business, and it is easy and inexpensive to set-up but it is growing very slowly in developing countries, and this study developed a paint formulation which gives better quality and good application properties. The effect of rheology modifiers, i.e. non-ionic polymers hydrophobically-modified ethoxylated urethanes (HEUR), anionic polymers hydrophobically-modified alkali soluble emulsions (HASE) and hydroxyl ethyl cellulose (HEC) on the quality and properties of water-based paints have been investigated. HEC provides the in-can viscosity and increases open working time while HASE improves application properties like spatter resistance and brush loading and HEUR provides excellent scrub resistance. Four paint recipes were prepared using four different thickeners HEC, HASE (carbopol) and Cellulose nitrate. The fourth formulation was thickened with a combination of HASE and HEC, this aimed at improving quality and at the same time reducing cost. The four samples were tested for quality tests such viscosity, sag resistance, volatile matter, tinter effect, drying times, hiding power, scrub resistance and stability on storage. Environmental factors were incorporated in the attempt to formulate an economic and green product. Hydroxyl ethyl cellulose and cellulose nitrate gave high quality and good properties of the paint. HEC and Cellulose nitrate showed stability on storage whereas carbopol thickener was very unstable.

Keywords: properties, thickeners, rheology modifiers, water based paints

Procedia PDF Downloads 150