Web based interface for numerical simulations of nonlinear evolution equations
Foster, Ryan Napoleon
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In Computational Science and Parallel Computing research, model equations have been developed to assist in solving problems in science and engineering. Such equations have aided researchers in developing methods used in the study of weather prediction, optical fiber communication systems, water waves, etc... Often, it is the desire of many researchers to further develop numerical methods and make these model equations, their numerical simulations and plots accessible to users through the Internet. In this thesis, I present a web based graphical user numerical simulation interface for nonlinear evolution equations such as the nonlinear Schrödinger (NLS), coupled NLS (CNLS), and the complex modified Korteweg-de Vries (CMKdV) equations. In addition, the numerical implementation of a proposed numerical scheme for the modified CNLS equation is presented. Sequential and parallel algorithms for such equations were implemented on sequential and multiprocessor machines. Index Words: Numerical Simulation, Nonlinear Schrödinger (NLS) equation, Coupled Nonlinear Schrödinger (CNLS) equation, Complex Modified Korteweg-de Vries (CMKdV) equation, Web based graphical user interface.