181 research outputs found
A comparative study of the AHP and TOPSIS methods for implementing load shedding scheme in a pulp mill system
The advancement of technology had encouraged mankind to design and create useful
equipment and devices. These equipment enable users to fully utilize them in various
applications. Pulp mill is one of the heavy industries that consumes large amount of
electricity in its production. Due to this, any malfunction of the equipment might
cause mass losses to the company. In particular, the breakdown of the generator
would cause other generators to be overloaded. In the meantime, the subsequence
loads will be shed until the generators are sufficient to provide the power to other
loads. Once the fault had been fixed, the load shedding scheme can be deactivated.
Thus, load shedding scheme is the best way in handling such condition. Selected load
will be shed under this scheme in order to protect the generators from being
damaged. Multi Criteria Decision Making (MCDM) can be applied in determination
of the load shedding scheme in the electric power system. In this thesis two methods
which are Analytic Hierarchy Process (AHP) and Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS) were introduced and applied. From this thesis,
a series of analyses are conducted and the results are determined. Among these two
methods which are AHP and TOPSIS, the results shown that TOPSIS is the best
Multi criteria Decision Making (MCDM) for load shedding scheme in the pulp mill
system. TOPSIS is the most effective solution because of the highest percentage
effectiveness of load shedding between these two methods. The results of the AHP
and TOPSIS analysis to the pulp mill system are very promising
Block method for third order ordinary differential equations
The problem of third order ordinary differential equations (ODEs) is solved directly by using the block backward differentiation formula. The block method is constructed by utilizing three back values and by differentiating the interpolating polynomial once, twice and thrice. Two approximated solutions are generated concurrently for each integration step. Numerical results indicate the efficiency of the direct method than the usual approach of transforming it into the first order ODEs
Parallel block backward differentiation formulas for solving large systems of ordinary differential equations.
In this paper, parallelism in the solution of Ordinary
Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology.
Parallelism is obtained by using Message Passing Interface (MPI).Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation
Componentwise block partitioning: a new strategy to solve stiff ordinary differential equations
Componentwise Block Partitioning is a new strategy to solve stiff ODEs, based on Block Backward Differentiation Formulas (BBDFs), and block of Adam type formulas. In this partitioning technique, the ODEs system is initially solved by Adam formulas until the equation that cause instability and stiffness is identified. Then, the equations that caused instability are placed into stiff subsystem and solved using BBDF. Numerical comparisons with code in the literature such as ode15s show the efficiency of the proposed partitioning technique
Block backward differentiation formulas for solving second order fuzzy differential equations
In this paper, we study the numerical method for solving second order Fuzzy Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF) under generalized concept of higher-order fuzzy differentiability. Implementation of the method using Newton iteration is discussed. Numerical results obtained by BBDF are presented and compared with Backward Differential Formulas (BDF) and exact solutions. Several numerical examples are provided to illustrate our methods
Modified block Runge-Kutta methods with various weights for solving stiff ordinary differential equations
A modified block Runge-Kutta (MBRK) methods for solving first order stiff ordinary differential equations (ODEs) are developed. Three sets of weight are chosen and implemented to the proposed methods. Stability regions of the MBRK methods are analyzed. Performances of the MBRK methods in terms of accuracy and computational time are compared with the classical third order Runge-Kutta (RK3) method and modified weighted RK3 method based on Centroidal mean (MWRK3CeM). The numerical results show that the proposed methods outperformed the comparing methods. Comparisons between the sets of weight used are also examined
Development of a-stable block method for the solution of stiff ordinary differential equations
A fixed step-size multistep block method for stiff Ordinary Differential Equations (ODEs) using the 2-point Block Backward Differentiation Formulas (BBDF) with improved efficiency is established. The method is developed using Taylor’s series expansion. The order and the error constant of the method are determined. To validate the new method is suitable for solving stiff ODEs, the stability and convergence properties are discussed. Numerical results indicate that the new method produced better accuracy than the existing methods when sloving the same problems
Block backward differentiation formulas for solving fuzzy differential equations under generalized differentiability
In this paper, the fully implicit 2-point block backward differentiation formula and diagonally implicit 2-point block backward differentiation formula were developed under the interpretation of generalized differentiability concept for solving first order fuzzy differential equations. Some fuzzy initial value problems were tested in order to demonstrate the performance of the developed methods. The approximated solutions for both methods were in good agreement with the exact solutions. The numerical results showed that the diagonally implicit method outperforms the fully implicit method in term of accuracy
Derivation of BBDF-α for solving ordinary differential equation
In this paper, the block backward differentiation formulas with parameter α (BBDF-α) of order three is derived in a constant step size for solving system of first order ordinary differential equations (ODEs). The coefficients of formula are generated using Maple software package. The influence of parameter α is considered to produce better approximate solutions at two points simultaneously. Numerical experiment is included to show the capability of the derived method in solving ODEs. Numerical results indicate that the BBDF-α outperforms the existing methods in term of accuracy
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