• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2004년도 학술대회지
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• International Journal of Automotive Technology
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• 제8권2호
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• pp.249-258
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• 2007

This paper proposes a method that can be used for the resistance estimation of a PWM (Pulse Width Modulation)-driven solenoid. By using estimated solenoid resistance, the PWM duty ratio was compensated to be proportional to the solenoid current. The proposed method was developed for use with EHB (Electro-Hydraulic Braking) systems, which are essential features of the regenerative braking system of many electric vehicles. Because the HU (Hydraulic Unit) of most EHB systems performs not only ABS/TCS/ESP (Electronic Stability Program) functions but also service braking function, the possible duration of continuous solenoid driving is so long that the generated heat can drastically change the level of solenoid resistance. The current model of the PWM-driven solenoid is further developed in this paper; from this a new resistance equation is derived. This resistance equation is solved by using an iterative method known as the FPT (fixed point theorem). Furthermore, by taking the average of the resistance estimates, it was possible to successfully eliminate the effect of measurement noise factors. Simulation results showed that the proposed method contained a sufficient pass-band in the frequency response. Experimental results also showed that adaptive solenoid driving which incorporates resistance estimations is able to maintain a linear relationship between the PWM duty ratio and the solenoid current in spite of a wide variety of ambient temperatures and continuous driving.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.197-214
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• 2021

In this paper, we have studied dynamics of fractional order mathematical model of malaria transmission for two groups of human population say semi-immune and non-immune along with growing stages of mosquito vector. The present fractional order mathematical model is the extension of integer order mathematical model proposed by Ousmane Koutou et al. For this study, Atangana-Baleanu fractional order derivative in Caputo sense has been implemented. In the view of memory effect of fractional derivative, this model has been found more realistic than integer order model of malaria and helps to understand dynamical behaviour of malaria epidemic in depth. We have analysed the proposed model for two precisely defined set of parameters and initial value conditions. The uniqueness and existence of present model has been proved by Lipschitz conditions and fixed point theorem. Generalised Euler method is used to analyse numerical results. It is observed that this model is more dynamic as we have considered all classes of human population and mosquito vector to analyse the dynamics of malaria.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.137-162
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• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.