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In this paper, with the aid of Matlab software, more exact solutions are obtained for coupled nonlinear schrödinger equations, by using a direct and efficient trigonometric function transform method. Finally, it is easy to derive the corresponding exact solutions of the uncoupled NLS equations in fiber optics.
In today's technological era, technologies for drawing fine figures have become necessary for effective communication in areas such as scientific research, industry, architecture, medical service, and education. In the areas of scientific research and education, computer algebra system (CAS) has become the preferred tool because of its superb drawing utilities and symbolic computation capabilities...
We investigate the integration of C implementation of fast arithmetic operations into MAPLE, focusing on triangular decomposition algorithms. We show substantial improvements over existing MAPLE implementations; our code also outperforms MAGMA on many examples. Profiling data show that data conversion can become a bottleneck for some algorithms, leaving room for further improvements.
Although the limit of a function at a point is one of the most important concepts in mathematics, to prove symbolically its formal definition is a challenging exercise that requires a certain level of expertise usually out of the capabilities of most students. This paper introduces a new mathematica package to prove symbolically the values of limits of functions in terms of delta and epsiv. In addition...
The ability of multi-core processors to increase application performance depends on the use of multiple threads within applications. Symbolic computations, requiring both CPU power and large memory, are well-suited candidates for deriving advantages from multi-core parallel architectures. This is possible only if the specific libraries and tools are designed to allow multi-threading and multi-processes...
The paper focuses on means of defining parameterized type categories and algorithms built on such types in Mathematica. Symbolic algorithms based on category theory have the advantage of systematically dealing with domains, categories, operators over them by creating general contexts of expressing algorithms, which can be applied by parameterizing them with various domains, using the same algorithm...
Summary form only given. Symbolic computation is not just helpful, it is very nearly a prerequisite for building models of complex objects that will be used in dynamic system simulators such as the virtual test bed (VTB). The reason that symbolic computation is so necessary is that, for reasons of compuatational speed, the code of any VTB model having natural coupling ports must directly express the...
This panel contribution presents an integrated approach that combines symbolic and numeric computations to investigate dynamic analysis and simulation issues in power systems. Power system studies including load flow and local bifurcation analysis, require the numerical solution of non-linear equations using the Newton-Raphson-Seydel technique. This algorithm requires the computation of higher order...
This paper describes the history and use of symbolic computation in power systems, from the tools used for power system analysis such as power flows, to its application in the class room to facilitate the explanation and understanding of complex models and concepts such as device modeling and simulation. An example of the use of symbolic computation to develop a basic power flow program with the help...
We have presented a new Matlab toolbox for robust control synthesis by symbolic computation. It is based on a parameter space approach accomplished by quantifier elimination and also equipped with a machinery for numerical simulation of the properties in a frequency domain. The toolbox is explained with several examples.
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