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1	Numerical methods for a four dimensional hyperchaotic system with applications Sibiya, Abram Hlophane 05 1900 (has links) This study seeks to develop a method that generalises the use of Adams-Bashforth to solve or treat partial differential equations with local and non-local differentiation by deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting solution is then transformed back into the real space by using the inverse Laplace transform. This is a powerful numerical algorithm for fractional order derivative. The error analysis for the method is studied and presented. The numerical simulations of the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the wave equation are presented. In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes that eventually caused chaotic behaviour (butterfly attractor) are shown. The related graphical simulations that show the existence of fractal structure that is characterised by chaos and usually called strange attractors are provided. For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer and fractional derivative orders. / Mathematical Sciences / M. Sc. (Applied Mathematics) Chaotic system Hyperchaotic system Ordinary differential equation Initial value problem Laplace transform Adams-Bashforth Fractional calculus Atangana-Baleanu Partial differential equation Fractional differential equation 518.4 Initial value problems Laplace transformation Fractional calculus Differential equations, Partial Fractional differential equations

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Numerical methods for a four dimensional hyperchaotic system with applications