Relevant bibliographies by topics / Newton-Raphson division

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Newton-Raphson division'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Newton-Raphson division"

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Parker, A., and J. O. Hamblen. "Optimal value for the Newton-Raphson division algorithm." Information Processing Letters 42, no. 3 (May 1992): 141–44. http://dx.doi.org/10.1016/0020-0190(92)90137-k.

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Schulte, M. J., J. Omar, and E. E. Swartzlander. "Optimal initial approximations for the Newton-Raphson division algorithm." Computing 53, no. 3-4 (September 1994): 233–42. http://dx.doi.org/10.1007/bf02307376.

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Kim, Myungsun. "Private Division over FHE-Encrypted Data using Newton-Raphson Approximation." Journal of Security Engineering 15, no. 3 (June 30, 2018): 189–204. http://dx.doi.org/10.14257/jse.2018.06.05.

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Montuschi, P., L. Ciminiera, and A. Giustina. "Division unit with Newton-Raphson approximation and digit-by-digit refinement of the quotient." IEE Proceedings - Computers and Digital Techniques 141, no. 6 (1994): 317. http://dx.doi.org/10.1049/ip-cdt:19941386.

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Shen, Yun-fu, Peng-fei Hu, and Xiao-ling Fan. "Principle of MSD floating-point division based on Newton-Raphson method on ternary optical computer." Journal of Shanghai University (English Edition) 15, no. 5 (October 2011): 347–51. http://dx.doi.org/10.1007/s11741-011-0749-3.

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Singh, Naginder, and Trailokya Nath Sasamal. "Design and Synthesis of Single Precision Floating Point Division based on Newton-Raphson Algorithm on FPGA." MATEC Web of Conferences 57 (2016): 01009. http://dx.doi.org/10.1051/matecconf/20165701009.

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Mu`ñoz, Daniel M., Diego F. Sanchez, Carlos H. Llanos, and Mauricio Ayala-Rincón. "Tradeoff of FPGA Design of a Floating-point Library for Arithmetic Operators." Journal of Integrated Circuits and Systems 5, no. 1 (November 21, 2010): 42–52. http://dx.doi.org/10.29292/jics.v5i1.309.

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Many scientific and engineering applications require to perform a large number of arithmetic operations that must be computed in an efficient manner using a high precision and a large dynamic range. Commonly, these applications are implemented on personal computers taking advantage of the floating-point arithmetic to perform the computations and high operational frequencies. However, most common software architectures execute the instructions in a sequential way due to the von Neumann model and, consequently, several delays are introduced in the data transfer between the program memory and the Arithmetic Logic Unit (ALU). There are several mobile applications which require to operate with a high performance in terms of accuracy of the computations and execution time as well as with low power consumption. Modern Field Programmable Gate Arrays (FPGAs) are a suitable solution for high performance embedded applications given the flexibility of their architectures and their parallel capabilities, which allows the implementation of complex algorithms and performance improvements. This paper describes a parameterizable floating-point library for arithmetic operators based on FPGAs. A general architecture was implemented for addition/subtraction and multiplication and two different architectures based on the Goldschmidt’s and the Newton-Raphson algorithms were implemented for division and square root. Additionally, a tradeoff analysis of the hardware implementation was performed, which enables the designer to choose, for general purpose applications, the suitable bit-width representation and error associated, as well as the area cost, elapsed time and power consumption for each arithmetic operator. Synthesis results have demonstrated the effectiveness of the implemented cores on commercial FPGAs and showed that the most critical parameter is the dedicated Digital Signal Processing (DSP) slices consumption. Simulation results were addressed to compute the mean square error (MSE) and maximum absolute error demonstrating the correctness of the implemented floating-point library and achieving and experimental error analysis. The Newton-Raphson algorithm achieves similar MSE results as the Goldschmidt’s algorithm, operating with similar frequencies; however, the first one saves more logic area and dedicated DSP blocks.
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Zia, Ehsan, Ebrahim Farshidi, and Abdolnabi Kosarian. "New digital background calibration method for pipelined ADCs." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 4 (June 4, 2020): 871–84. http://dx.doi.org/10.1108/compel-10-2019-0396.

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Purpose Pipelined analog-to-digital converters (ADCs) are widely used in electronic circuits. The purpose of this paper is to propose a new digital background calibration method to correct the capacitor mismatch, finite direct current (DC) gain and nonlinearity of residue amplifiers in pipelined ADCs. Design/methodology/approach The errors are corrected by defining new functions based on generalized Newton–Raphson algorithm. Although the functions have analytical solutions, an iterative procedure is used for calibration. To accelerate the calibration process, proper initialization for the errors is identified by using evaluation estimation block and solving inverse matrix. Findings Several behavioral simulations of a 12-bit 100MS/s pipelined ADC in MATLAB indicate that signal-to-(noise + distortion) ratio (SNDR) and spurious free dynamic range (SFDR) are improved from 30dB/33dB to 70dB/79dB after calibration. Calibration is achieved in approximately 2,000 clock cycles. Practical implications The digital part of the proposed method is implemented on field-programmable gate array to validate the performance of the pipelined ADC. The experimental result shows that the degradation of SNDR, SFDR, integral nonlinearity, differential nonlinearity and effective number of bits is negligible according to fixed-point operation vs floating-point in simulation results. Originality/value The novelty of this study is to use Newton–Raphson algorithm combined with appropriate initialization to reduce the number of divisions as well as calibration time, which is suitable in the recent nano-meter complementary metal oxide semiconductor technologies.
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Laman Trip, Diederik S., and Wessel N. van Wieringen. "A parallel algorithm for ridge-penalized estimation of the multivariate exponential family from data of mixed types." Statistics and Computing 31, no. 4 (May 17, 2021). http://dx.doi.org/10.1007/s11222-021-10013-x.

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AbstractComputationally efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g., binary and continuous) as special case of interest. The model parameter is estimated by maximization of the pseudo-likelihood augmented with a convex penalty. The estimator is shown to be consistent. With a world of multi-core computers in mind, a computationally efficient parallel Newton–Raphson algorithm is presented for numerical evaluation of the estimator alongside conditions for its convergence. Parallelization comprises the division of the parameter vector into subvectors that are estimated simultaneously and subsequently aggregated to form an estimate of the original parameter. This approach may also enable efficient numerical evaluation of other high-dimensional estimators. The performance of the proposed estimator and algorithm are evaluated and compared in a simulation study. Finally, the presented methodology is applied to data of an integrative omics study.
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Verma, Amit K., Narendra Kumar, and Diksha Tiwari. "Haar wavelets collocation method for a system of nonlinear singular differential equations." Engineering Computations ahead-of-print, ahead-of-print (July 31, 2020). http://dx.doi.org/10.1108/ec-04-2020-0181.

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Purpose The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations: −(tk1y′(t))′=t−ω1f1(t,y(t),z(t)), −(tk2z′(t))′=t−ω2f2(t,y(t),z(t)),where t > 0, subject to the following initial values, boundary values and four-point boundary values: y(0)=γ1, y′(0)=0, z(0)=γ2, z′(0)=0, y′(0)=0, y(1)=δ1, z′(0)=0, z(1)=δ2, y(0)=0, y(1)=n1z(v1), z(0)=0, z(1)=n2y(v2),where n1,n2,v1,v2∈(0,1) and k1≥0, k2≥0, ω1<1, ω2<1, γ1, γ2, δ1, δ2 are real constants. Design/methodology/approach To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques. Findings The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems. Originality/value The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering.
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Dissertations / Theses on the topic "Newton-Raphson division"

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Pettersson, Stefan. "Implementation and evaluation of a polynomial-based division algorithm." Thesis, Linköping University, Department of Electrical Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1900.

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In comparison to other basic arithmetic operations, such as addition, subtraction and multiplication,division is far more complex and expensive. Many division algorithms, except for lookup tables, rely on recursion with usually complex operations in the loop. Even if the cost in terms of area and computational complexity sometimes can be made low, the latency is usually high anyway, due to the number of iterations required. Therefore, in order to find a faster method and a method that provides better precision, a non-recursive polynomial-based algorithm was developed by the Department of Electrical Engineering at Linköping University.

After having performed high-level modelling in Matlab, promising results were achieved for up to 32 bits of accuracy. However, since the cost model did not take in account other factors that are important when implementing in hardware, the question remained whether the division algorithm was also competitive in practice or not. Therefore, in order to investigate that, this thesis work was initiated.

This report describes the hardware implementation, the optimization and the evaluation of this division algorithm, regarding latency and hardware cost for numbers with different precisions. In addition to this algorithm, the common Newton-Raphson algorithm has also been implemented, to serve as a reference.

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Panhaleux, Adrien. "Contributions à l'arithmétique flottante : codages et arrondi correct de fonctions algébriques." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00744373.

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Une arithmétique sûre et efficace est un élément clé pour exécuter des calculs rapides et sûrs. Le choix du système numérique et des algorithmes arithmétiques est important. Nous présentons une nouvelle représentation des nombres, les "RN-codes", telle que tronquer un RN-code à une précision donnée est équivalent à l'arrondir au plus près. Nous donnons des algorithmes arithmétiques pour manipuler ces RN-codes et introduisons le concept de "RN-code en virgule flottante." Lors de l'implantation d'une fonction f en arithmétique flottante, si l'on veut toujours donner le nombre flottant le plus proche de f(x), il faut déterminer si f(x) est au-dessus ou en-dessous du plus proche "midpoint", un "midpoint" étant le milieu de deux nombres flottants consécutifs. Pour ce faire, le calcul est d'abord fait avec une certaine précision, et si cela ne suffit pas, le calcul est recommencé avec une précision de plus en plus grande. Ce processus ne s'arrête pas si f(x) est un midpoint. Étant donné une fonction algébrique f, soit nous montrons qu'il n'y a pas de nombres flottants x tel que f(x) est un midpoint, soit nous les caractérisons ou les énumérons. Depuis le PowerPC d'IBM, la division en binaire a été fréquemment implantée à l'aide de variantes de l'itération de Newton-Raphson dues à Peter Markstein. Cette itération est très rapide, mais il faut y apporter beaucoup de soin si l'on veut obtenir le nombre flottant le plus proche du quotient exact. Nous étudions comment fusionner efficacement les itérations de Markstein avec les itérations de Goldschmidt, plus rapides mais moins précises. Nous examinons également si ces itérations peuvent être utilisées pour l'arithmétique flottante décimale. Nous fournissons des bornes d'erreurs sûres et précises pour ces algorithmes.
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Hu, ShiQiang, and Qingxin Yan. "Inversion of Vandermonde Matrices in FPGAs." Thesis, Linköping University, Department of Electrical Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2648.

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In this thesis, we explore different algorithms for the inversion of Vandermonde matrices and the corresponding suitable architectures for implement in FPGA. The inversion of Vandermonde matrix is one of the three master projects of the topic, Implementation of a digital error correction algorithm for time-interleaved analog-to-digital converters. The project is divided into two major parts: algorithm comparison and optimization for inversion of Vandermonde matrix; architecture selection for implementation. A CORDIC algorithm for sine and cosine and Newton-Raphson based division are implemented as functional blocks.

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Book chapters on the topic "Newton-Raphson division"

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Pandey, Pawan Kumar, Dilip Singh, and Rajeevan Chandel. "Fixed-Point Divider Using Newton Raphson Division Algorithm." In Lecture Notes in Electrical Engineering, 225–34. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0275-7_19.

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Véstias, Mário P., and Horácio C. Neto. "Decimal Division Using the Newton–Raphson Method and Radix-1000 Arithmetic." In Embedded Systems Design with FPGAs, 31–54. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1362-2_2.

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Conference papers on the topic "Newton-Raphson division"

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Rao, Dhage Navaneet, Ganne Sai Charan, Degala Veera Venkata Sairam, and Kamatchi S. "Posit Number Division using Newton-Raphson method." In 2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT). IEEE, 2021. http://dx.doi.org/10.1109/icaect49130.2021.9392582.

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Muller, Jean-Michel. "Avoiding double roundings in scaled Newton-Raphson division." In 2013 Asilomar Conference on Signals, Systems and Computers. IEEE, 2013. http://dx.doi.org/10.1109/acssc.2013.6810304.

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Vestias, M´rio P., and Hor´cio C. Neto. "Revisiting the Newton-Raphson Iterative Method for Decimal Division." In 2011 International Conference on Field Programmable Logic and Applications (FPL). IEEE, 2011. http://dx.doi.org/10.1109/fpl.2011.33.

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Louvet, Nicolas, Jean-Michel Muller, and Adrien Panhaleux. "Newton-Raphson algorithms for floating-point division using an FMA." In 2010 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP). IEEE, 2010. http://dx.doi.org/10.1109/asap.2010.5540948.

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Nenadic, N. M., and S. B. Mladenovic. "Fast Division on Fixed-Point DSP Processors Using Newton-Raphson Method." In EUROCON 2005 - The International Conference on "Computer as a Tool". IEEE, 2005. http://dx.doi.org/10.1109/eurcon.2005.1630028.

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Majumdar, Alok, Helen Cole, and C. P. Chen. "Numerical Modeling of Flow Distribution in Microfluidics Systems." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77378.

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This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.
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Meng, Xianghui, and Youbai Xie. "Numerical Study of Piston Skirt-Liner Elastohydrodynamic Lubrication and Contact by the Multigrid Method." In ASME 2010 Internal Combustion Engine Division Fall Technical Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/icef2010-35097.

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The cylinder liner-piston system of internal combustion engines is one of the key friction pairs running at the most rigor working conditions. Under the influence of elastohydrodynamic lubrication and contact between the piston skirt and the liner, the dynamic process of piston is a nonlinear and stiff problem difficult to be analyzed accurately and easily. To reach a stable and rapid convergence in analysis, the MEBDF method and the multigrid method are used to solve the piston-skirt elastohydrodynamic lubrication and contact problem. Firstly the solving process of the piston dynamics is analyzed based on the MEBDF method. Then the residual equations for the elastohydrodynamic lubrication pressure are built based on the multigrid method. And the solving method of the nonlinear residual equations is presented based on the quasi Newton-Raphson method. Finally the numerical simulation program is developed based on the MEBDF method and the multigrid method. The elastohydrodynamic lubrication and contact problem of the piston skirt-liner system is simply analyzed based on the simulation. The study in this paper can provide an effective method for tribological analysis and optimization of piston–liner system in the future.
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Abbaspour, Mohammad, Kirby S. Chapman, Larry A. Glasgow, and Zhongquan C. Zheng. "Dynamic Simulation of Gas-Liquid Homogeneous Flow in Natural Gas Pipeline Using Two-Fluid Conservation Equations." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77136.

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Homogeneous two-phase flows are frequently encountered in a variety processes in the petroleum and gas industries. In natural gas pipelines, liquid condensation occurs due to the thermodynamic and hydrodynamic imperatives. During horizontal, concurrent gas-liquid flow in pipes, a variety of flow patterns can exist. Each pattern results from the particular manner by which the liquid and gas distribute in the pipe. The objective of this study is to simulate the non-isothermal, one-dimensional, transient homogenous two-phase flow gas pipeline system using two-fluid conservation equations. The modified Peng-Robinson equation of state is used to calculate the vapor-liquid equilibrium in multi-component natural gas to find the vapor and liquid compressibility factors. Mass transfer between the gas and the liquid phases is treated rigorously through flash calculation, making the algorithm capable of handling retrograde condensation. The liquid droplets are assumed to be spheres of uniform size, evenly dispersed throughout the gas phase. The method of solution is the fully implicit finite difference method. This method is stable for gas pipeline simulations when using a large time step and therefore minimizes the computation time. The algorithm used to solve the nonlinear finite-difference thermo-fluid equations for two phase flow through a pipe is based on the Newton-Raphson method. The results show that the liquid condensate holdup is a strong function of temperature, pressure, mass flow rate, and mixture composition. Also, the fully implicit method has advantages, such as the guaranteed stability for large time step, which is very useful for simulating long-term transients in natural gas pipeline systems.
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Beladi, Behnaz, and Hendrik C. Kuhlmann. "Flow Over a Sudden Expansion in an Annular Pipe: Steady Axisymmetric Flow and its Stability." In ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fedsm2016-7896.

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The stability of the axisymmetric incompressible Newtonian flow in an annular pipe suddenly expanding radially inward is investigated. The axisymmetric steady basic flow is discretized using primitive variables and second-order finite volumes on a staggered grid. The resulting algebraic equations are solved by Newton–Raphson iteration. A three-dimensional global linear stability analysis is performed. The solutions to the linear stability problem are represented by normal modes. The generalized eigenvalue problem is solved using an implicitly restarted Arnoldi algorithm which is provided by the ARPACK library and a Cayley transformation. Stability boundaries have been computed for a range of parameters varying the outlet radius ratio. The physical instability mechanisms are studied by a an posteriori analysis of the kinetic energy transferred between the basic state and the critical mode. Neutral curves and critical modes are presented and the instability mechanisms are discussed.
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Dashti, Mehrnoosh, Ali Asghar Hamidi, and Ali Asghar Mozafari. "Performance and Exhaust Emission Characteristics of a Spark Ignition Engine Operated With Gasoline and CNG Blend." In ASME 2012 Internal Combustion Engine Division Spring Technical Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ices2012-81179.

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Using CNG as an additive for gasoline is a proper choice due to higher octane number of CNG enriched gasoline with respect to that of gasoline. As a result, it is possible to use gasoline with lower octane number in the engine. This would also mean the increase of compression ratio in SI engines resulting in higher performance and lower gasoline consumption. Over the years, the use of simulation codes to model the thermodynamic cycle of an internal combustion engine have developed tools for more efficient engine designs and fuel combustion. In this study, a thermodynamic cycle simulation of a conventional four-stroke spark-ignition engine has been developed. The model is used to study the engine performance parameters and emission characteristics of CNG/gasoline blend fuelled engine. A spark ignition engine cycle simulation based on the first law of thermodynamic has been developed by stepwise calculations for compression process, ignition delay time, combustion and expansion processes. The building blocks of the model are mass and energy conservation equations. Newton-Raphson method has been used to solve the equations numerically and there was no need to solve them analytically. In the quasi-dimensional combustion model, the cylinder is divided into two zones separated by a thin flame front. The flame front propagates spherically throughout the combustion chamber to the point that it contacts the cylinder wall and head. The model effectively describes the thermodynamic processes and chemical state of the working fluid via a closed system containing compression, combustion, and expansion processes. The model predicts the trends and tradeoffs the performance characteristics at various engine speeds. The variation of indicated power, ISFC and emissions are predicted by the model. Experimental data are also presented to indicate the validity of the model. The predicted results based on the model have shown reasonable agreement with the corresponding experimental data.
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