The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.
Abstract:In this paper, we present Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to obtain approximate solutions for differential equations related with heat transfer phenomena. Comparing figures between approximate and exact solutions, show the effectiveness of the method.
This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we show the effectiveness of the proposed method.
Four continuous-time strategies to improve the speed-accuracy-power tradeoff in CMOS amplifiers by using low-power offset-compensation circuits are presented. The offset contribution at the output voltage is extracted and used to modify the DC component of the input voltage or the value of the active load, through low frequency feedback loops, which are realized using two transistors operating in weak inversion and a small capacitor. Because these circuits do not affect the bandwidth and allow using small transistors, the power consumption is greatly reduced with respect to an uncompensated amplifier of the same speed and offset behavior. The proposed strategies present reduced costs in area, power consumption and complexity, and a decrease in the low frequency noise contributions. MonteCarlo, HSPICE simulations results of common source, class AB and fully differential amplifiers, and experimental results of a class AB amplifier, all implemented in a 0.5-lm CMOS technology are shown. Statistical analyses of these strategies are also presented. Improvements up to 99.74% and 398.6% in the offset and the power consumption are respectively observed.
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