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CLASSES OF HIGHER ORDER CONVERGENT ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS
FAROOQ AHMED SHAH The Korean Society for Computational and Applied M 2024 Journal of applied and pure mathematics Vol.6 No.3
In this paper, we suggest and analyze new higher order classes of iterative methods for solving nonlinear equations by using variational iteration technique. We present several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.
FAROOQ AHMED SHAH,TAYYAB ZAMIR,EHSAN UL HAQ,IQRA ABID The Korean Society for Computational and Applied M 2024 Journal of applied and pure mathematics Vol.6 No.3
This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.
Farooq Mujahid,Ahmed Ammar,Qureshi Kamran,Shah Ajmal,Waheed Khalid,Siddique Waseem,Irfan Naseem,Ahmad Masroor,Farooq Amjad 한국원자력학회 2022 Nuclear Engineering and Technology Vol.54 No.9
Owing to the rising concerns about the safety of nuclear power plants (NPP), it is essential to study the venturi scrubber in detail, which is a key component of the filtered containment venting system (FCVS). FCVS alleviates the pressurein containment byfiltering and venting out the contaminated air. Themain objective of this research was to perform a CFD investigation of different configurations of a circular, non-submerged, selfpriming venturi scrubber to estimate and improve the performance in the removal of elemental iodine from the air. For benchmarking, a mass transfer model which is based on two-film theory was selected and validated by experimental data where an alkaline solution was considered as the scrubbing solution. This mass transfer model was modified and implemented on a unique formation of two self-priming venturi scrubbers in series. Euler-Euler method was used for two-phase modeling and the realizable K ε model was used for capturing the turbulence. The obtained results showed a remarkable improvement in the removal of radioactive iodine from the air using a series combination of venturi scrubbers. The removal efficiency was improved at every single data point.
Classes of higher order convergent iterative methods for solving nonlinear equations
Farooq Ahmed Shah 한국전산응용수학회 2024 Journal of Applied and Pure Mathematics Vol.6 No.3
In this paper, we suggest and analyze new higher order classes of iterative methods for solving nonlinear equations by using variational iteration technique. We present several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.
Farooq Ahmed Shah,Tayyab Zamir,Ehsan ul Haq,Iqra Abid 한국전산응용수학회 2024 Journal of Applied and Pure Mathematics Vol.6 No.3
This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.
Farooq Ahmed,Tae Jo Ko,Lee Jongmin,Yein Kwak,In Jun Yoon,S. Thirumalai Kumaran 한국정밀공학회 2021 International Journal of Precision Engineering and Vol.22 No.7
Materials with high hardness are usually difficult to machine, and accomplishing precise and economical machining depends on all the cutting conditions. Appropriate tool geometry is one important aspect for the cutting process that can be optimized based on the machining parameters. In this study, the finite element simulation method was applied to analyze the effects of tool geometry on the cutting forces and tool temperature during the ball end milling of tool steel (AISI H13). Multiobjective optimization of the geometrical parameters was performed using the grey relational method, which gave a set of input parameters to obtain the minimum cutting forces and temperature. The findings of this work could be used as a basis for tool design. Experiments were conducted with mono-objective and multi-objective optimal geometries to validate the finite element analysis. The finite element and experimental results were both congruous with an error limit of 5%.
Farooq Ahmed(아흐매드파루크),Ji Hyeon Byeon(변지현),Ki Moon Park(박기문),Tae Jo Ko(고태조) 한국기계가공학회 2017 한국기계가공학회지 Vol.16 No.4
When considering the proper function and life cycle length of a product, its surface finish plays an important role. This experimental study was carried out to understand the effect of input factors on surface roughness and how it can be minimized by controlling the input parameters. This experimental work was performed by machining the surface of STD 61 blocks with a surface inclined at 30° by ball end-milling and optimizing the input parameters using the Taguchi technique. Signal-to-Noise (S/N) ratio and analysis of variance (ANOVA) were applied to find the significance of the input parameters. The optimum level of input parameters to minimize surface roughness was obtained.