 # Block backward differentiation formulas for solving first and second order fuzzy differential equations

## Citation

Tiaw, Kah Fook (2016) Block backward differentiation formulas for solving first and second order fuzzy differential equations. Masters thesis, Universiti Putra Malaysia.

## Abstract

In this thesis, the concerns are mainly in modifying existence method of Block Backward Differentiation Formula (BBDFs) for solving first order fuzzy differential equation, second order non-stiff and stiff fuzzy differential equations (FDEs). This method will solve the Initial Value Problems (IVPs) of FDEs using constant step size. The first part of the thesis discussed the combination of BBDF and Block Simpson into Hybrid method for solving first order FDEs. The subsequent part of the thesis focuses on the modification of BBDF into fuzzy version of BBDF for solving second order non-stiff FDEs and second orders stiff FDEs. Algorithm was developed to run the FDEs problems in Microsoft Visual C++ environment to obtain exact and approximate solutions. The algorithm of existing BBDF was modified into fuzzy version. The BBDFs method approximates the solution at two points concurrently. Therefore, numerical results show that the proposed methods reduce the execution time when compared to the Backward Differentiation Formula (BDF). In order to compute the error norm, the difference between the approximate solutions and the exact solutions was calculated. The numerical results also show the proposed method produces smaller errors when compared to modified Euler method. The accuracy of the solutions obtained by BBDF and BDF are comparable particularly when the finer step sizes are used. However, in term of execution time, the proposed method BBDF outperformed BDF method. The solutions obtained were illustrated by graphs. In conclusion, the numerical results clearly demonstrate the efficiency of using BBDF methods proposed in this study for solving fuzzy differential equations. From the results of tests problems, the modified BBDF method reveals that the execution time has been reduced and the numerical result is accurate, which proves its superiority on the existing methods.  Preview
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