THE NUMERICAL STABILITIES OF MULTIDERIVATIVE BLOCK METHOD

In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomialsP(h) and Q(h) in the stability functions h(h)=P(h)/Q(h)are given. Furthermore, we prove P(-h)-Q(h). With the aid of symbolic computations and the expressions of diagonal Fade approximations, we obtained the biggest block size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM,l>1)

High Order Block Method for Third Order ODEs

Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.

Runge-Kutta Method and Bolck by Block Method to Solve Nonlinear Fredholm-Volterra Integral Equation with Continuous Kernel

In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.

Two-Step Hybrid Block Method for Solving Nonlinear Jerk Equations

In this paper, a block method with one hybrid point for solving Jerk equations is presented. The hybrid point is chosen to optimize the local truncation errors of the main formulas for the solution and the derivative at the end of the block. Analysis of the method is discussed, and some numerical examples show that the proposed method is efficient and accurate.

Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.

A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations

In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.

Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type using Hybrid Block Method

Neutral Delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their application in biological and physiological processes.A fifth-order two-point hybrid implicit multistep block method(2PIH5)has been formulated in this research for the numerical solution of Neutral Delay Differential Equation(NDDE).A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5.The order,consistency,and zero-stability for 2PIH5 have been illustrated.The analyses of convergence and stability test have been performed and discussed.The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method.Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE.The proposed method is proved to be comparable with the other existing methods.It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

A Generalized Block-by-block Method for the System of Linear Volterra Integral Equations of the Second Kind

In this paper, we provide a generalized block-by-block method for constructing block-by-block systems to solve the system of linear Volterra integral equations of the second kind, and then deduce some of the special cases. Compared with the expansion method and He＇s homotopy perturbation method, respectively numerical examples are given to certify the effectiveness of the method. The results show that the block-by-block method is very effective, simple, and of high accuracy in solving the system of linear Volterra integral equations of the second kind.

THE NUMERICAL STABILITY OF THE BLOCK θ-METHODS FOR DELAY DIFFERENTIAL EQUATIONS

This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.

BLOCK BIDIAGONALIZATION METHODS FOR MULTIPLE NONSYMMETRIC LINEAR SYSTEMS

The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.

BLOCK PIVOT METHODS FOR SOLVING FRICTIONAL CONTACT PROBLEMS

Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.

A CLASS OF r-POINT (r+1)ST-ORDER A-STABLE ONE-BLOCK METHODS WITH DAMPING AT THE INFINITE POINT

This paper presents a class of r-point (r+1)st-order A-stable one-block methods with damping at the infinite point (DIAOB r,r+1 ). Under the conditions of the same order, A-stability, operation count (at each iterative step) and storage space are the same as the methods in , the methods in the paper improve the stability in a neighborhood at the infinite point. And, by using the OOPI method , it possesses much faster rate of convergence for solving systems of nonlinear equations produced by the DIAOB r,r+1 .

OPTIMIZATION AND METHOD OF DRAWING CONTROL IN BLOCK CAVING AT TONGKUANGYU MINE

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A BLOCK VARIANT OF THE GMRES METHOD FOR UNSYMMETRIC LINEAR SYSTEMS

Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s. m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.

高放废物处置缓冲材料砌块养护方法研究

在高放废物地质处置库中,作为阻滞核素迁移的关键环节,缓冲材料通常以高压实砌块形式放置于废物罐周围。为了保证砌块的工程性能,缓冲材料砌块在制备、储存、运输和安装等各阶段均应进行环境湿度控制,以减少环境湿度对砌块性能的劣化影响。以高庙子膨润土压实试样为研究对象,开展了裸样、覆膜、覆膜+密封等不同包装方式,在0~100%相对湿度环境下的长期养护性能测试。试验结果表明:针对含水率介于13%~15%之间的膨润土压实试样,当环境湿度在80%~92%养护时,试样的质量变化均不超过1%;其中在92%的环境湿度下,试样的质量变化不超过0.3%,为最优养护环境。采用覆膜+密封包装方式,可大幅拓宽环境湿度范围,试样在不同相对湿度下的质量变化大幅减少,当相对湿度超过57%后,试样的质量变化比均不超过1%。其中在相对湿度为92%的养护环境下,试样的质量变化比最小,仅为0.032%。研究结果可为解决米级尺度高放废物地质处置缓冲材料大型砌块长期存储这一难题提供基础参数和技术支撑。

Economic Valuation of Auctioned Tourist Hunting Blocks in Tanzania

Economic valuation of ecosystems is increasingly being recognized as an important exercise to inform sustainable utilization and conservation of natural assets. It helps in planning and establishing fair profit margins that accrue either directly or indirectly from the consumptive and non-consumptive uses of ecosystem goods and services. This paper is based on a study which estimated the economic values of tourist hunting blocks (HBs) in Tanzania using the Analytic Multicriteria Valuation Method (AMUVAM). The study used a sample size of 12 out of 24 vacant hunting blocks which were to be auctioned to potential hunting companies in December 2022. The economic values of HBs were estimated using the time horizon of 10 years (the mean tenure for winning company). The results show that the economic values ranged from USD 6,215,588 to USD 653,470,695 per hunting block and the Existence Value (EV) constituted about 19% of the Total Economic Value (TEV). EV ranged from USD 632,210 to USD 125,147,285. The study underscores the need for decisions to allocate ecosystems, such as HBs, to both direct and indirect uses, to be guided by a though understanding of their values. We further recommend building the capacity of staff charged with the role of managing and allocating uses of these ecosystems to enable them undertake economic valuation of ecosystems using both simple and more robust analytical tools, such as the GIS, relational databases, and worldwide websites based tools, like InVEST (Integrated Valuation of Environmental Services and Tradeoffs), ARIES (Artificial Intelligence for Ecosystem Services), and Co$ting Nature.

Clinical Observation on Brachial Plexus Block with “One Injection Two Points” Method Guiding by Ultrasound

OBJECTIVE: To compare the clinical effect of brachial plexus block with "One Injection Two Points" guided under ultrasound and the conventional method guiding by ultrasound. METHODS: 70 patients were randomized evenly into 2 groups, with 35 patients in each group, while the Experiment Group(Group B) received One Injection Two Points" method, the Control Group(Group A) received the conventional method.The nerve block every 5 s, the success rate of anesthesia, the dosage of local anesthetics, second remedial anesthesia, adverse reactions, etc.were recorded. RESULTS: Group B was superior to group A in the success rate of anesthesia; There were 6 patients in group A who required constant pump injection of Remifentanil to remedy, while no patients in Group B needed remedy treatment. There were no serious adverse reactions in both groups.CONCLUSIONS: The clinical effect of brachial plexus block with "One Injection Two Points" method guided under ultrasoundguiding by ultrasound was superior to that of the conventional method.

马鞍山长江公铁大桥主航道桥中塔下横梁施工关键技术

马鞍山长江公铁大桥主航道桥Z4号中塔采用空间四肢A形钢-混组合塔,横向两塔肢间设下横梁,下横梁间设3道系梁,纵向两塔肢间不设置横梁。下横梁采用支架法分层浇筑施工。下横梁施工支架采用落地式钢管支架配套模板体系,受力性能满足要求;通过有限元计算比选下横梁混凝土分层浇筑方案并进行优化,采取(5.5+2.5)m分层方案,上、下层混凝土分别分为2块、3块分层分块浇筑;通过低温升、易泵送、高抗裂的C60混凝土研制、下横梁与塔柱倒弧结合面抗裂措施优化、分块间接缝构造形式及施工工艺优化、下横梁与系梁混凝土浇筑施工组织优化、混凝土温度智能化监控、预应力束张拉时机控制等混凝土防裂措施,有效解决了下横梁大体积混凝土易开裂的难题。

阶段矿房法二步骤采场地压控制研究

在阶段矿房二步骤开采时,为了减小上盘岩移量,常采纳采场中部切槽并向上盘、下盘两侧回采,从而缩短采场暴露时间,以便减小上盘岩移量。当地压达到流变发生的条件后,缩短采场暴露时间并不能有效控制上盘巷道发生岩移破坏。为此,利用三维连续体快速拉格朗日分析数值模拟采场上盘地压,并根据流变理论分析,采纳低松弛预应力大直径钢绞线锚索支护上盘顶板以便减小上盘地压,从而克服发生流变变形的应力条件。结果表明:在上盘岩体上施加支护抗力可减小或消除高地压导致的流变变形;采纳7排7.0 m长的锚索、每排6根支护上盘顶板后大幅度减小了上盘岩移量,但采场第2分层上排锚索及一步骤采场第3分层局部锚索的锚固力超过设计值;采纳8排7.0 m长的锚索、一步骤采场每排7根、二步骤采场每排6根支护上盘顶板后,即使回采底柱,锚索锚固力也不会达到设计值。监测表明,大直径钢绞线锚索支护后上盘岩移量减小到一般不超过6 mm。