Transformasi Fourier Multiplikatif Dan Aplikasinya Pada Persamaan Diferensial Multiplikatif

This research is a development of multiplicative calculus. This study is about the Fourier multiplicative transformation and its application to the multiplicative differential equation. This study aims to determine the Fourier multiplicative transformation as well as the multiplicative differential equation. This study contains numerical simulations to solve the problem of ordinary multiplicative differential equations of the first order. The methods used in this research are descriptive research methods through the study of literature. The results of this study are the application of multiplicative Fourier transformations to multiplicative differential equations and numerical solutions of ordinary multiplicative differential equations with the Adam Bashforth-Moulton multiplicative method.  Keywords: Multiplicative Calculus, Fourier Multiplicative Transformation, Multiplicative Differential Equations, Adams Bashforth Moulton Multiplicative Metho

Wong-Zakai method for stochastic differential equations in engineering

In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Alartiyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can he used as an alternative for the known approximation techniques for stochastic models

Calculations of rate constants for the three-body recombination of H2 in the presence of H2

A new global potential energy hypersurface for H2 + H2 is constructed and quasiclassical trajectory calculations performed using the resonance complex theory and energy transfer mechanism to estimate the rate of three body recombination over the temperature range 100 to 5000 K. The new potential is a faithful representation of ab initio electron structure calculations, is unchanged under the operation of exchanging H atoms, and reproduces the accurate H3 potential as one H atom is pulled away. Included in the fitting procedure are geometries expected to be important when one H2 is near or above the dissociation limit. The dynamics calculations explicitly include the motion of all four atoms and are performed efficiently using a vectorized variable-stepsize integrator. The predicted rate constants are approximately a factor of two smaller than experimental estimates over a broad temperature range

Real-time simulation of dynamic vehicle models using high performance reconfigurable computing platforms

A software-based approach for Real-Time Simulation (RTS) may have difficulties in meeting real-time constraints for complex models. In this thesis, we present a methodology for the design and implementation of RTS algorithms, based on the use of Field-Programmable Gate Array (FPGA) technology to improve the response time of these models. Our methodology utilizes traditional Hardware/Software co-design approaches to generate a heterogeneous architecture for an FPGA-based simulator. We have optimized the hardware design such that it efficiently utilizes the parallel nature of FPGAs and pipelines the independent operations. Further enhancement is obtained through the use of custom accelerators for common non-linear functions. Since the systems we examine have relatively low response time requirements, our approach greatly simplifies the software components by porting the computationally complex regions to hardware. We illustrate the partitioning of a hardware-based simulator design across dual FPGAs, initiate RTS using a system input from a Hardware-in-the-Loop (HIL) framework, and use these simulation results from our FPGA-based platform to perform response analysis. The total simulation time, which includes the time required to receive the system input over a socket (without HIL), software initialization, hardware computation, and transfer of simulation results back over a socket, shows a speedup of 2x as compared to a similar setup with no hardware acceleration. The correctness of the simulation output from the hardware has also been validated with the simulated results from the software-only design