AN ENHANCED WAVELET BASED METHOD FOR NUMERICAL SOLUTION OF HIGH ORDER BOUNDARY VALUE PROBLEMS

The Legendre wavelet collocation method (LWCM) is suggested in this study for solving high-order boundary value problems numerically. Eighth, tenth, and twelfth-order examples are used as test problems to ensure that the technique is efficient and accurate. In comparison to other approaches, the numerical results obtained using LWCM demonstrate that the method's accuracy is very good. The results indicate that the method requires less computational effort to achieve better results

Quintic spline collocation method for fractional boundary value problems

AbstractThe spline collocation method is a competent and highly effective mathematical tool for constructing the approximate solutions of boundary value problems arising in science, engineering and mathematical physics. In this paper, a quintic polynomial spline collocation method is employed for a class of fractional boundary value problems (FBVPs). The FBVPs are expressed in terms of Caputo’s fractional derivative in this approach. The consistency relations are derived in order to compute the approximate solutions of FBVPs. Finally, numerical results are given, which demonstrate the effectiveness of the numerical scheme

Three Point Spline Collocation Method for Solving General Linear and Nonlinear Eighth-Order Boundary-Value Problems

In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords the spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh. Numerical results are given for four examples to illustrate the implementation and efficiency of the method.  Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient. يتم في هذا البحث تطوير طريقة شرائحية لإيجاد الحل العددي لمسائل القيم الحدية الخطية وغير الخطية في المعادلات التفاضلية المعممة من المرتبة الثامنة. الطريقة المقترحة تقدم الحل الشرائحي التقريبي باستخدام كثيرة حدود من الدرجة إحدى عشرة وتلك الحدودية تحقق المسائل الحدية والابتدائية المطروحة في ثلاث نقاط تجميع. تبين الدراسة أن الطريقة المقترحة عندما تطبق لحل هذه المسائل تكون موجودة ومعرفة بشكل وحيد. كما تظهر الدراسة التحليلية أن الطريقة تكون متجانسة ومتقاربة وأن الخطأ المقتطع الشامل من الرتبة إحدى عشرة. تم اختبار الطريقة الشرائحية بحل أربع مسائل مختلفة، حيث تشير المقارنات لنتائج طريقتنا مع نتائج الطرائق الأخرى إلى أفضلية الطريقة المقترحة من حيث الدقة والفعالية

Three Point Spline Collocation Method for Solving General Linear and Nonlinear Eighth-Order Boundary-Value Problems

In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords the spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh. Numerical results are given for four examples to illustrate the implementation and efficiency of the method.  Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient. يتم في هذا البحث تطوير طريقة شرائحية لإيجاد الحل العددي لمسائل القيم الحدية الخطية وغير الخطية في المعادلات التفاضلية المعممة من المرتبة الثامنة. الطريقة المقترحة تقدم الحل الشرائحي التقريبي باستخدام كثيرة حدود من الدرجة إحدى عشرة وتلك الحدودية تحقق المسائل الحدية والابتدائية المطروحة في ثلاث نقاط تجميع. تبين الدراسة أن الطريقة المقترحة عندما تطبق لحل هذه المسائل تكون موجودة ومعرفة بشكل وحيد. كما تظهر الدراسة التحليلية أن الطريقة تكون متجانسة ومتقاربة وأن الخطأ المقتطع الشامل من الرتبة إحدى عشرة. تم اختبار الطريقة الشرائحية بحل أربع مسائل مختلفة، حيث تشير المقارنات لنتائج طريقتنا مع نتائج الطرائق الأخرى إلى أفضلية الطريقة المقترحة من حيث الدقة والفعالية

طريقة شرائحية بثلاثة وسطاء تجميع لحل مسائل في المعادلات التفاضلية المعممة من المرتبة التاسعة خاضعة لشروط حدية.

يتم في هذا العمل استخدام كثيرات حدود شرائحية من الدرجة الحادية عشرة مع ثلاث نقاط تجميع لتطوير طريقة لحساب الحل العددي ومشتقاته حتى المرتبة التاسعة لمسائل القيم الحدية الخطية وغير الخطية في المعادلات التفاضلية المعممة من المرتبة التاسعة. تبين الدراسة أن الطريقة الشرائحية المقترحة عندما طُبِقتْ بثلاث نقاط تجميع لهذه المسائل كانت موجودة ومعرفة بشكل وحيد. كما تظهر الدراسة التحليلية للتقارب أن الطريقة المقترحة مستقرة ومتناسقة من الرتبة الحادية عشرة وتملك معدل تقارب يزيد عن ستة. كما تم اختبار الطريقة الشرائحية بحل بعض المسائل التطبيقية، إذ تشير المقارنات لنتائجنا مع نتائج عددية لبعض الطرائق المذكورة في مراجع أخرى حديثة إلى أفضلية النتائج التي توصلنا إليها من حيث الاستقرار والدقة العددية. In this paper, we use polynomial splines of eleventh degree with three collocation points to develop a method for computing approximations to the solution and its derivatives up to ninth order for general linear and nonlinear ninth-order boundary-value problems (BVPs). The study shows that the spline method with three collocation points when is applied to these problems is existent and unique. We prove that the proposed method if applied to ninth-order BVPs is stable and consistent of order eleven, and it possesses convergence rate greater than six. Finally, some numerical experiments are presented for illustrating the theoretical results and by comparing the results of our method with the other methods, we reveal that the proposed method is better than others

A computational method for nonlinear 2m‐th order boundary value problems

In this paper, two point boundary value problems of 2mth‐order nonlinear differential equations are considered. The existence of the solution and a new iterative algorithm which is large‐range convergent are proposed for the problems in reproducing kernel space. The advantage of the approach must lie in the fact that, on the one hand, for the arbitrary fixed initial value function, the iterative method is convergent. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives, respectively. Some examples are displayed to demonstrate the computation efficiency of the method. Foundation item: Supported by National Natural Science Foundation of China (No. 60572125); Heilongjiang Institute of Science and Technology (No. 07–17); Heilongjiang province education department science and technology (No. 11531324). First published online: 10 Feb 201

Control of the turbulent flow in a plane diffuser through optimized contoured cavities

A passive control strategy, which consists in introducing contoured cavities in solid walls, is applied to a plane asymmetric diffuser at a Reynolds number that implies fully-turbulent flow upstream of the diffuser divergent part. The analysed reference configuration, for which experimental and numerical data were available, is characterized by an area ratio of 4.7 and a divergence angle of 10 degrees. A large zone of steady flow separation is present in the diffuser without the introduction of the control. One and two subsequent contoured cavities are introduced in the divergent wall of the diffuser and a numerical optimization procedure is carried out to obtain the cavity geometry that maximizes the pressure recovery in the diffuser and minimizes the flow separation extent. The introduction of one optimized cavity leads to an increase in pressure recovery of the order of 6.9% and to a significant reduction of the separation extent, and further improvement (9.6%) is obtained by introducing two subsequent cavities in the divergent wall. The most important geometrical parameters are also identified, and the robustness of the solution to small changes in their values and in the Reynolds number is assessed. The present results show that the proposed control strategy, previously tested in the laminar regime, is effective also for turbulent flows at higher Reynolds numbers. As already found for laminar flow, the success of the control is due both to a virtual geometry modification of the diffuser and to a favourable effect of the cavities in reducing the momentum losses near the wall

Dynamics of face and annular seals with two-phase flow

A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. Some of the distinctive behavior characteristics of two phase seals are discussed, particularly their axial stability. The main conclusions are that seals with two phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction: calculations of stiffness coefficients, temperature and pressure distributions, and leakage rates for parallel and coned face seals. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two phase flow is described and documented. The analyses, results, and computer codes are summarized

Monitoring damage in concrete using diffuse ultrasonic coda wave interferometry

The prevalence of concrete and cement-based materials in the civil infrastructure plus the risk of failure makes structural health monitoring an important issue in the understanding of the complete life cycle of civil structures. Correspondingly, the field of nondestructive evaluation (NDE) has been maturing and now concentrates on the detection of flaws and defects, as well as material damage in early stages of degradation. This defect detection is typically usually done by looking at the impulse response of the medium in question such as a cement-based material. The impulse response of a solid can be used to image a complex medium. Classically, the waveform is obtained by an active setup: an ultrasonic signal is generated at one location and recorded at another location. The waveform obtained from imaging can be used to quantitatively characterize the medium, for example by calculating the material's diffusivity coefficient or dissipation rate. In recent years, a different monitoring technique has been developed in seismology to measure the velocity of different kinds of waves, the Coda Wave Interferometry (CWI). In this CWI technique, the main focus is given to the late part of the recorded waveform, the coda. CWI is now successfully used in seismology and acoustics. In the current research, CWI is applied on concrete in different damage states to develop basic knowledge of the behavior of the wave velocity, and how it can be used to characterize cement-based materials. By comparing two impulse responses, the relative velocity change between the two impulse responses is used to characterize damage. Because of the stress-dependency of the velocity change, the calculations can also be used to directly calculate the Murnaghan's and Lam´e's coefficients. The newer technique of CWI is applied - the Stretching Technique (ST) [27]. The first goal of this research is to establish the viability of using CWI in cement-based materials. Next, we use the ST in the application of stress as we compress concrete samples for the detection of thermal damage, ASR-damage and mechanical softening.M.S.Committee Chair: Jacobs, Laurence J.; Committee Member: Kim, Jin-Yeon; Committee Member: Sabra, Karim G

Registration and categorization of camera captured documents

Camera captured document image analysis concerns with processing of documents captured with hand-held sensors, smart phones, or other capturing devices using advanced image processing, computer vision, pattern recognition, and machine learning techniques. As there is no constrained capturing in the real world, the captured documents suffer from illumination variation, viewpoint variation, highly variable scale/resolution, background clutter, occlusion, and non-rigid deformations e.g., folds and crumples. Document registration is a problem where the image of a template document whose layout is known is registered with a test document image. Literature in camera captured document mosaicing addressed the registration of captured documents with the assumption of considerable amount of single chunk overlapping content. These methods cannot be directly applied to registration of forms, bills, and other commercial documents where the fixed content is distributed into tiny portions across the document. On the other hand, most of the existing document image registration methods work with scanned documents under affine transformation. Literature in document image retrieval addressed categorization of documents based on text, figures, etc. However, the scalability of existing document categorization methodologies based on logo identification is very limited. This dissertation focuses on two problems (i) registration of captured documents where the overlapping content is distributed into tiny portions across the documents and (ii) categorization of captured documents into predefined logo classes that scale to large datasets using local invariant features. A novel methodology is proposed for the registration of user defined Regions Of Interest (ROI) using corresponding local features from their neighborhood. The methodology enhances prior approaches in point pattern based registration, like RANdom SAmple Consensus (RANSAC) and Thin Plate Spline-Robust Point Matching (TPS-RPM), to enable registration of cell phone and camera captured documents under non-rigid transformations. Three novel aspects are embedded into the methodology: (i) histogram based uniformly transformed correspondence estimation, (ii) clustering of points located near the ROI to select only close by regions for matching, and (iii) validation of the registration in RANSAC and TPS-RPM algorithms. Experimental results on a dataset of 480 images captured using iPhone 3GS and Logitech webcam Pro 9000 have shown an average registration accuracy of 92.75% using Scale Invariant Feature Transform (SIFT). Robust local features for logo identification are determined empirically by comparisons among SIFT, Speeded-Up Robust Features (SURF), Hessian-Affine, Harris-Affine, and Maximally Stable Extremal Regions (MSER). Two different matching methods are presented for categorization: matching all features extracted from the query document as a single set and a segment-wise matching of query document features using segmentation achieved by grouping area under intersecting dense local affine covariant regions. The later approach not only gives an approximate location of predicted logo classes in the query document but also helps to increase the prediction accuracies. In order to facilitate scalability to large data sets, inverted indexing of logo class features has been incorporated in both approaches. Experimental results on a dataset of real camera captured documents have shown a peak 13.25% increase in the F–measure accuracy using the later approach as compared to the former