Jacob, Kavikumar and Mamat, Mustafa and Amir Hamzah, Nor Shamsidah and Ahmad, Noor'Aini and Lee, Siaw Chong (2012) *An impulsive approach for numerical investigation of hybrid fuzzy differential equations and intuitionistic treatment for fuzzy ordinary and partial differential equations.* Other thesis, Universiti Tun Hussein Onn Malaysia.

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## Abstract

Many evolution processes are characterized by the fact that at certain moments of time, they experience a change of state abruptly. It is assume naturally, that those perturbations act instantaneously, in the form of impulses. The impulsive differential equations, by means differential equations involving impulse effects, are seen as a natural description of observed evolution phenomenon of several real world problems. For example, systems with impulse effect have applications in physics, biotechnolagy, industrial robotics, pharmacokinetics, population dynamics, ecology, optimal control production theory and many others. Therefore, it is beneficial to study the theory of impulsive differential equations as a well deserved discipline, due to the increase applications of impulsive differential equations in various fields in the future. However, in many mathematical modelling of the real world problems, fuzziness and impulsiveness occurs simultaneously. This problem would be better modelled by impulsive fuzzy differential equations. Therefore, this research applies the theory of impulsive fuzzy differential equations by combining the theories of impulsive differential equations and fuzzy differential equations. The numerical algorithms are developed and the solutions are verified by comparing the results with the analytical solutions. The novel method for the first order linear impulsive hzzy differential equations under generalized differentiability is also proposed analytically and numerically, The convergence theor~m for the impulsive fuzzy differential equations (FDE) under generalized differentiability is defined. In this study, Ant Colony Programming (ACP) was used to find the optimal solution of FDE. Results obtained show that the method is effective in solving fuzzy differential equation. The solution in this method is equivaIent to the exact solution of the problem. Modified Romberg's method and Modified Two-step Simpson's 318 method are used to solve FDE with hzzy IVP has been successfully derived. The result has been shown that Modified Rornberg's method gave smaller error than the Standard Euler's method. Therefore Modified Romberg's method can estimate the solution of fizzy differential equation more effectively than the Euler's method in solving fuzzy differential equation. Meanwhile, by using the modified wo-step Simpson's 318 methods, it has been shown that the solution of FDE provide more accurate approximation to the exact solution and it also gives better results than the Runge-Kutta method. In other words, Modified Twostep Simpson's 318 method is an effective method to solve fuzzy differential equation compared to the Runge-Kutta method.

Item Type: | Thesis (Other) |
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Subjects: | T Technology > TJ Mechanical engineering and machinery > TJ210.2-211 Mechanical devices and figures. Automata. Ingenious mechanisms. |

ID Code: | 6879 |

Deposited By: | Normajihan Abd. Rahman |

Deposited On: | 07 May 2015 15:19 |

Last Modified: | 07 May 2015 15:19 |

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