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Mesh Free Collocation Method for Numerical Solution of Initial-Boundary-Value Problems Using Radial Basis Functions

Thesis Info

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Author

Arshed Ali

Program

PhD

Institute

Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

City

Swabi

Province

KPK

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Applied Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2886/1/334S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726632807

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Nonlinear partial differential equations are often used to understand and model nonlinear processes arising in many branches of science and engineering. For most of partial differential equations a general closed-form analytical solution is not available and therefore use of numerical methods always remains an important alternative for the solution of partial differential equations. Several numerical methods are developed for the solution of partial differential equations including finite difference methods, finite element methods, spectral methods and spline methods. However numerical methods posses some limitations such as mesh generation, slow rate of convergence, spatial dependence, stability, low accuracy and difficult to implement in complex geometries. One of domain type methods is known as radial basis functions method, which is a truly meshless method, infinitely differentiable, numerically accurate, stable, very high rate of convergence, spatial independence and flexible with respect to complex geometry. The main difference between the mesh free radial basis functions method and classical mesh-based methods is that the radial basis functions can be extended to the entire domain of influence without diving into elements. In this thesis, we present mesh free radial basis functions method based on collocation principle for numerical solution of various time dependent nonlinear partial differential equations namely, Regularized Long Wave (RLW) equation, Modified Regularized Long Wave (MRLW) equation, Modified Equal Width Wave (MEW) equation, Klein- Gordon Schrödinger (KGS) equations, Klein-Gordon Zakharov (KGZ) equations, Two dimensional Coupled Burgers’ equations and Two dimensional Reaction-Diffusion Brusselator equations. Different radial basis functions are used for this purpose. First order forward and second order central difference approximation is employed to the time derivative. The elementary stability and convergence of the proposed method are discussed. Accuracy of the method is assessed in terms of various error norms, number of nodal points and time step size. Performance of the proposed method is validated through examples from literature. Apart from ease of implementation, better accuracy is obtained. Comparison with existing methods such as finite difference methods, finite element methods, boundary element methods and spline methods is made to show the superiority and simple applicability of the mesh free method.
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اہلیہ سید ابوالحسن علی ندوی

اہلیہ سید ابوالحسن علی ندوی
۱۵ دسمبر کو مجلسِ عاملہ کے صدر، مولانا سید ابوالحسن علی ندوی مدظلہ کی اہلیہ محترمہ کا انتقال ہوگیا، جو بڑی نیک بخت اور عابدہ، زاہدہ خاتون تھیں․․․․․․ اﷲ تعالیٰ مرحومہ کی مغفرت فرمائے اور حضرت مولانا کے غم و اندوہ کو زایل کرے، آمین۔
(ضیاء الدین اصلاحی، جنوری ۱۹۹۰ء)

Analysis of Consumer Assessment in Small and Medium Enterprises

Raja Abon Makmur Lestari's business has good potential, resulting in considerable business competition. One of the businesses that produce shredded is Small and Medium Enterprises (UKM) Raja Abon Makmur Lestari. This business must apply a consumer-oriented marketing concept. The application of this concept is to determine the marketing mix consisting of product, price, promotion, and place. The purpose of this study was to analyze consumer assessments of the various attributes of shredded products and evaluate the results of the shredded product marketing mix strategy. The method used in this research is descriptive analysis, with the 4P marketing mix approach. The marketing mix strategy evaluation design involves internal parties, namely business owners, and external parties, namely consumers. The results of the discussion show that consumer assessment of products has guaranteed quality, consumer ratings of prices are in accordance with quality, consumer assessments of shredded product distribution are easy to obtain and consumer assessments of promotion by word of mouth are very efficient and easy to get information on social media. The evaluation results of the marketing mix for shredded products are in the range of 101-125. Based on this total value, it can be concluded that all the variables of the marketing mix carried out by the king of shredded and prosperous sustainable have been effective.

Mitigation of Drought Stress in Maize Hybrid Through Different Nutrient Management Strategies

Macronutrients (N, P, and K) along with micronutrients particularly zinc promote successful crop growth under drought stress. Zinc (Zn) is an essential micronutrient involved in photosynthesis and as an enzyme antioxidant-cofactor. Its deficiency may cause severe growth reduction and may also delay the crop maturity. Drought stress is the principal threat to crop productivity worldwide. Approximately, one third of the cultivated area of the world suffers from perpetual drought. Drought stress is an alarming global issue with severe consequence to human well being. In Pakistan, yield of maize (Zea mays L.) is often reduced by drought, and the severity of the problem may increase due to the protected climate change. Therefore, developing different approaches to mitigate drought stress are inevitable to minimize the losses in crop production. This study was conducted at the Agronomic Research Area, University of Agriculture, Faisalabad, Pakistan during spring of 2013/2014. For this, a 2-year field study was conducted to assess the effects of drought on maize hybrid growth, productivity, and yield level changing, etc. It was adjusted as a randomized complete block design to assess the yield variation of the hybrid maize involving a split plot arrangement with three replications. Three soil moisture regimes were maintained as main plot and included: (I1) well-watered treatment, (I2) mild drought with 25 mm of potential soil moisture deficit (PSMD), and (I3) severe drought with 50 mm of PSMD. Nutrients levels were laid out as sub-plots and included:T1 (Control), T2 (200 kg ha-1 N), T3 (300 kg ha-1 N), T4 (12 kg ha-1 Zn), T5 (200 kg ha-1 N + 12 kg ha-1 Zn), T6 (300 kg ha-1 N + 12 kg ha-1 Zn) in first experiment, while in 2nd experiment sub plots treatments were as follows (T1) control, (T2) 100 kg ha-1 K, (T3) 150 kg ha-1 K, (T4) 12 kg ha-1 Zn, (T5) 100 kg ha-1 K + 12 kg ha-1 Zn, and (T6) 150 kg ha-1 K + 12 kg ha-1 Zn.All of the allometric and agronomic parameters like leaf area index, leaf area duration, crop growth rate, plant population, number of grain rows cob-1 and 1000- grain weight were strongly affected by drought. Obtained results were showed that application of Zn with higher doses of N and K strongly improved of the maize root growth, and it was the most cost-effective approach under drought stress conditions. The highest grains yield of (8.57 t ha-1 and 8.12 t ha-1 in 2013 and 8.76 t ha-1 and 8.04 t ha-1 in 2014) were obtained by (I1T6) treatment combination which was resulted in well-watered and fertilized plot with higher doses of nutrients during 2013/2014. Hence, higher rates of N and K with Zn can be used to enhance maize production and net income under well-watered field conditions.